%!PS-Adobe-2.0
%%Creator: dvips(k) 5.95a Copyright 2005 Radical Eye Software
%%Pages: 18
%%PageOrder: Ascend
%%BoundingBox: 0 0 595 842
%%DocumentFonts: CMBX12 CMR10 CMCSC10 CMMI10 CMR7 CMMI7 CMR12 CMMI12
%%+ MSBM10 CMMI8 CMTI12 CMR8 CMSY10 CMTI10 CMR9 CMEX10 CMSY8 CMMI6 CMBX8
%%+ CMR6 MSAM10 CMSY6 MSBM7 CMBX10 CMTT10
%%DocumentPaperSizes: a4
%%EndComments
%DVIPSWebPage: (www.radicaleye.com)
%DVIPSCommandLine: /localapp/tetex-3.0/bin/dvips.real -f
%DVIPSParameters: dpi=600, compressed
%DVIPSSource:  TeX output 2006.01.09:1153
%%BeginProcSet: texc.pro 0 0
%!
/TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S
N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72
mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0
0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{
landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize
mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[
matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round
exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{
statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0]
N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin
/FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array
/BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2
array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N
df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A
definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get
}B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub}
B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr
1 add N}if}B/id 0 N/rw 0 N/rc 0 N/gp 0 N/cp 0 N/G 0 N/CharBuilder{save 3
1 roll S A/base get 2 index get S/BitMaps get S get/Cd X pop/ctr 0 N Cdx
0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx
sub Cy .1 sub]/id Ci N/rw Cw 7 add 8 idiv string N/rc 0 N/gp 0 N/cp 0 N{
rc 0 ne{rc 1 sub/rc X rw}{G}ifelse}imagemask restore}B/G{{id gp get/gp
gp 1 add N A 18 mod S 18 idiv pl S get exec}loop}B/adv{cp add/cp X}B
/chg{rw cp id gp 4 index getinterval putinterval A gp add/gp X adv}B/nd{
/cp 0 N rw exit}B/lsh{rw cp 2 copy get A 0 eq{pop 1}{A 255 eq{pop 254}{
A A add 255 and S 1 and or}ifelse}ifelse put 1 adv}B/rsh{rw cp 2 copy
get A 0 eq{pop 128}{A 255 eq{pop 127}{A 2 idiv S 128 and or}ifelse}
ifelse put 1 adv}B/clr{rw cp 2 index string putinterval adv}B/set{rw cp
fillstr 0 4 index getinterval putinterval adv}B/fillstr 18 string 0 1 17
{2 copy 255 put pop}for N/pl[{adv 1 chg}{adv 1 chg nd}{1 add chg}{1 add
chg nd}{adv lsh}{adv lsh nd}{adv rsh}{adv rsh nd}{1 add adv}{/rc X nd}{
1 add set}{1 add clr}{adv 2 chg}{adv 2 chg nd}{pop nd}]A{bind pop}
forall N/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn
/BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put
}if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{
bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A
mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{
SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{
userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X
1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4
index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N
/p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{
/Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT)
(LaserWriter 16/600)]{A length product length le{A length product exch 0
exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse
end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask
grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot}
imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round
exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto
fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p
delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M}
B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{
p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S
rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end

%%EndProcSet
%%BeginProcSet: texps.pro 0 0
%!
TeXDict begin/rf{findfont dup length 1 add dict begin{1 index/FID ne 2
index/UniqueID ne and{def}{pop pop}ifelse}forall[1 index 0 6 -1 roll
exec 0 exch 5 -1 roll VResolution Resolution div mul neg 0 0]FontType 0
ne{/Metrics exch def dict begin Encoding{exch dup type/integertype ne{
pop pop 1 sub dup 0 le{pop}{[}ifelse}{FontMatrix 0 get div Metrics 0 get
div def}ifelse}forall Metrics/Metrics currentdict end def}{{1 index type
/nametype eq{exit}if exch pop}loop}ifelse[2 index currentdict end
definefont 3 -1 roll makefont/setfont cvx]cvx def}def/ObliqueSlant{dup
sin S cos div neg}B/SlantFont{4 index mul add}def/ExtendFont{3 -1 roll
mul exch}def/ReEncodeFont{CharStrings rcheck{/Encoding false def dup[
exch{dup CharStrings exch known not{pop/.notdef/Encoding true def}if}
forall Encoding{]exch pop}{cleartomark}ifelse}if/Encoding exch def}def
end

%%EndProcSet
%%BeginProcSet: special.pro 0 0
%!
TeXDict begin/SDict 200 dict N SDict begin/@SpecialDefaults{/hs 612 N
/vs 792 N/ho 0 N/vo 0 N/hsc 1 N/vsc 1 N/ang 0 N/CLIP 0 N/rwiSeen false N
/rhiSeen false N/letter{}N/note{}N/a4{}N/legal{}N}B/@scaleunit 100 N
/@hscale{@scaleunit div/hsc X}B/@vscale{@scaleunit div/vsc X}B/@hsize{
/hs X/CLIP 1 N}B/@vsize{/vs X/CLIP 1 N}B/@clip{/CLIP 2 N}B/@hoffset{/ho
X}B/@voffset{/vo X}B/@angle{/ang X}B/@rwi{10 div/rwi X/rwiSeen true N}B
/@rhi{10 div/rhi X/rhiSeen true N}B/@llx{/llx X}B/@lly{/lly X}B/@urx{
/urx X}B/@ury{/ury X}B/magscale true def end/@MacSetUp{userdict/md known
{userdict/md get type/dicttype eq{userdict begin md length 10 add md
maxlength ge{/md md dup length 20 add dict copy def}if end md begin
/letter{}N/note{}N/legal{}N/od{txpose 1 0 mtx defaultmatrix dtransform S
atan/pa X newpath clippath mark{transform{itransform moveto}}{transform{
itransform lineto}}{6 -2 roll transform 6 -2 roll transform 6 -2 roll
transform{itransform 6 2 roll itransform 6 2 roll itransform 6 2 roll
curveto}}{{closepath}}pathforall newpath counttomark array astore/gc xdf
pop ct 39 0 put 10 fz 0 fs 2 F/|______Courier fnt invertflag{PaintBlack}
if}N/txpose{pxs pys scale ppr aload pop por{noflips{pop S neg S TR pop 1
-1 scale}if xflip yflip and{pop S neg S TR 180 rotate 1 -1 scale ppr 3
get ppr 1 get neg sub neg ppr 2 get ppr 0 get neg sub neg TR}if xflip
yflip not and{pop S neg S TR pop 180 rotate ppr 3 get ppr 1 get neg sub
neg 0 TR}if yflip xflip not and{ppr 1 get neg ppr 0 get neg TR}if}{
noflips{TR pop pop 270 rotate 1 -1 scale}if xflip yflip and{TR pop pop
90 rotate 1 -1 scale ppr 3 get ppr 1 get neg sub neg ppr 2 get ppr 0 get
neg sub neg TR}if xflip yflip not and{TR pop pop 90 rotate ppr 3 get ppr
1 get neg sub neg 0 TR}if yflip xflip not and{TR pop pop 270 rotate ppr
2 get ppr 0 get neg sub neg 0 S TR}if}ifelse scaleby96{ppr aload pop 4
-1 roll add 2 div 3 1 roll add 2 div 2 copy TR .96 dup scale neg S neg S
TR}if}N/cp{pop pop showpage pm restore}N end}if}if}N/normalscale{
Resolution 72 div VResolution 72 div neg scale magscale{DVImag dup scale
}if 0 setgray}N/psfts{S 65781.76 div N}N/startTexFig{/psf$SavedState
save N userdict maxlength dict begin/magscale true def normalscale
currentpoint TR/psf$ury psfts/psf$urx psfts/psf$lly psfts/psf$llx psfts
/psf$y psfts/psf$x psfts currentpoint/psf$cy X/psf$cx X/psf$sx psf$x
psf$urx psf$llx sub div N/psf$sy psf$y psf$ury psf$lly sub div N psf$sx
psf$sy scale psf$cx psf$sx div psf$llx sub psf$cy psf$sy div psf$ury sub
TR/showpage{}N/erasepage{}N/setpagedevice{pop}N/copypage{}N/p 3 def
@MacSetUp}N/doclip{psf$llx psf$lly psf$urx psf$ury currentpoint 6 2 roll
newpath 4 copy 4 2 roll moveto 6 -1 roll S lineto S lineto S lineto
closepath clip newpath moveto}N/endTexFig{end psf$SavedState restore}N
/@beginspecial{SDict begin/SpecialSave save N gsave normalscale
currentpoint TR @SpecialDefaults count/ocount X/dcount countdictstack N}
N/@setspecial{CLIP 1 eq{newpath 0 0 moveto hs 0 rlineto 0 vs rlineto hs
neg 0 rlineto closepath clip}if ho vo TR hsc vsc scale ang rotate
rwiSeen{rwi urx llx sub div rhiSeen{rhi ury lly sub div}{dup}ifelse
scale llx neg lly neg TR}{rhiSeen{rhi ury lly sub div dup scale llx neg
lly neg TR}if}ifelse CLIP 2 eq{newpath llx lly moveto urx lly lineto urx
ury lineto llx ury lineto closepath clip}if/showpage{}N/erasepage{}N
/setpagedevice{pop}N/copypage{}N newpath}N/@endspecial{count ocount sub{
pop}repeat countdictstack dcount sub{end}repeat grestore SpecialSave
restore end}N/@defspecial{SDict begin}N/@fedspecial{end}B/li{lineto}B
/rl{rlineto}B/rc{rcurveto}B/np{/SaveX currentpoint/SaveY X N 1
setlinecap newpath}N/st{stroke SaveX SaveY moveto}N/fil{fill SaveX SaveY
moveto}N/ellipse{/endangle X/startangle X/yrad X/xrad X/savematrix
matrix currentmatrix N TR xrad yrad scale 0 0 1 startangle endangle arc
savematrix setmatrix}N end

%%EndProcSet
%%BeginFont: CMSY10
%!PS-AdobeFont-1.1: CMSY10 1.0
%%CreationDate: 1991 Aug 15 07:20:57
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSY10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /minus put
dup 1 /periodcentered put
dup 14 /openbullet put
dup 18 /reflexsubset put
dup 20 /lessequal put
dup 21 /greaterequal put
dup 26 /propersubset put
dup 29 /greatermuch put
dup 50 /element put
dup 59 /emptyset put
dup 91 /union put
dup 92 /intersection put
dup 102 /braceleft put
dup 103 /braceright put
dup 106 /bar put
dup 110 /backslash put
dup 112 /radical put
readonly def
/FontBBox{-29 -960 1116 775}readonly def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMTT10
%!PS-AdobeFont-1.1: CMTT10 1.00B
%%CreationDate: 1992 Apr 26 10:42:42
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.00B) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMTT10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch true def
end readonly def
/FontName /CMTT10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 44 /comma put
dup 46 /period put
dup 47 /slash put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 53 /five put
dup 64 /at put
dup 67 /C put
dup 79 /O put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 103 /g put
dup 104 /h put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 121 /y put
dup 122 /z put
readonly def
/FontBBox{-4 -235 731 800}readonly def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMBX10
%!PS-AdobeFont-1.1: CMBX10 1.00B
%%CreationDate: 1992 Feb 19 19:54:06
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.00B) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMBX10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Bold) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMBX10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 52 /four put
dup 54 /six put
dup 55 /seven put
dup 56 /eight put
readonly def
/FontBBox{-301 -250 1164 946}readonly def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: MSBM7
%!PS-AdobeFont-1.1: MSBM7 2.1
%%CreationDate: 1992 Oct 17 08:30:50
% Math Symbol fonts were designed by the American Mathematical Society.
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (2.1) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (MSBM7) readonly def
/FamilyName (Euler) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /MSBM7 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 82 /R put
readonly def
/FontBBox{0 -504 2615 1004}readonly def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMSY6
%!PS-AdobeFont-1.1: CMSY6 1.0
%%CreationDate: 1991 Aug 15 07:21:34
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSY6) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY6 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /minus put
readonly def
/FontBBox{-4 -948 1329 786}readonly def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: MSAM10
%!PS-AdobeFont-1.1: MSAM10 2.1
%%CreationDate: 1993 Sep 17 09:05:00
% Math Symbol fonts were designed by the American Mathematical Society.
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (2.1) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (MSAM10) readonly def
/FamilyName (Euler) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /MSAM10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 3 /square put
readonly def
/FontBBox{8 -463 1331 1003}readonly def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMR6
%!PS-AdobeFont-1.1: CMR6 1.0
%%CreationDate: 1991 Aug 20 16:39:02
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR6) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR6 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 43 /plus put
dup 48 /zero put
dup 50 /two put
dup 51 /three put
readonly def
/FontBBox{-20 -250 1193 750}readonly def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMBX8
%!PS-AdobeFont-1.1: CMBX8 1.0
%%CreationDate: 1991 Aug 20 16:36:07
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMBX8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Bold) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMBX8 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 83 /S put
readonly def
/FontBBox{-59 -250 1235 750}readonly def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMMI6
%!PS-AdobeFont-1.1: CMMI6 1.100
%%CreationDate: 1996 Jul 23 07:53:52
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI6) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI6 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 100 /d put
readonly def
/FontBBox{11 -250 1241 750}readonly def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMSY8
%!PS-AdobeFont-1.1: CMSY8 1.0
%%CreationDate: 1991 Aug 15 07:22:10
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMSY8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY8 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /minus put
dup 48 /prime put
dup 50 /element put
dup 52 /triangle put
dup 91 /union put
dup 102 /braceleft put
dup 103 /braceright put
readonly def
/FontBBox{-30 -955 1185 779}readonly def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMEX10
%!PS-AdobeFont-1.1: CMEX10 1.00
%%CreationDate: 1992 Jul 23 21:22:48
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.00) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMEX10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMEX10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 0 /parenleftbig put
dup 1 /parenrightbig put
dup 18 /parenleftbigg put
dup 19 /parenrightbigg put
dup 22 /floorleftbigg put
dup 23 /floorrightbigg put
dup 80 /summationtext put
readonly def
/FontBBox{-24 -2960 1454 772}readonly def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMR9
%!PS-AdobeFont-1.1: CMR9 1.0
%%CreationDate: 1991 Aug 20 16:39:59
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR9) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR9 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 19 /acute put
dup 44 /comma put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 53 /five put
dup 54 /six put
dup 55 /seven put
dup 56 /eight put
dup 57 /nine put
dup 65 /A put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 70 /F put
dup 71 /G put
dup 72 /H put
dup 73 /I put
dup 75 /K put
dup 76 /L put
dup 77 /M put
dup 78 /N put
dup 79 /O put
dup 80 /P put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 85 /U put
dup 89 /Y put
dup 90 /Z put
readonly def
/FontBBox{-39 -250 1036 750}readonly def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMTI10
%!PS-AdobeFont-1.1: CMTI10 1.00B
%%CreationDate: 1992 Feb 19 19:56:16
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.00B) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMTI10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMTI10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 12 /fi put
dup 19 /acute put
dup 39 /quoteright put
dup 44 /comma put
dup 45 /hyphen put
dup 46 /period put
dup 65 /A put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 71 /G put
dup 73 /I put
dup 77 /M put
dup 79 /O put
dup 80 /P put
dup 81 /Q put
dup 83 /S put
dup 84 /T put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 106 /j put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 113 /q put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
dup 122 /z put
dup 127 /dieresis put
readonly def
/FontBBox{-163 -250 1146 969}readonly def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMR8
%!PS-AdobeFont-1.1: CMR8 1.0
%%CreationDate: 1991 Aug 20 16:39:40
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR8 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 12 /fi put
dup 40 /parenleft put
dup 41 /parenright put
dup 43 /plus put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 55 /seven put
dup 61 /equal put
dup 67 /C put
dup 80 /P put
dup 97 /a put
dup 99 /c put
dup 101 /e put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 108 /l put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
readonly def
/FontBBox{-36 -250 1070 750}readonly def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMTI12
%!PS-AdobeFont-1.1: CMTI12 1.0
%%CreationDate: 1991 Aug 18 21:06:53
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMTI12) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMTI12 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 12 /fi put
dup 14 /ffi put
dup 44 /comma put
dup 45 /hyphen put
dup 46 /period put
dup 49 /one put
dup 58 /colon put
dup 67 /C put
dup 70 /F put
dup 71 /G put
dup 73 /I put
dup 80 /P put
dup 82 /R put
dup 84 /T put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 113 /q put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
dup 122 /z put
readonly def
/FontBBox{-36 -251 1103 750}readonly def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMMI8
%!PS-AdobeFont-1.1: CMMI8 1.100
%%CreationDate: 1996 Jul 23 07:53:54
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI8 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 59 /comma put
dup 71 /G put
dup 82 /R put
dup 83 /S put
dup 100 /d put
dup 105 /i put
dup 110 /n put
dup 112 /p put
dup 114 /r put
readonly def
/FontBBox{-24 -250 1110 750}readonly def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: MSBM10
%!PS-AdobeFont-1.1: MSBM10 2.1
%%CreationDate: 1993 Sep 17 11:10:37
% Math Symbol fonts were designed by the American Mathematical Society.
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (2.1) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (MSBM10) readonly def
/FamilyName (Euler) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /MSBM10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 66 /B put
dup 82 /R put
dup 83 /S put
readonly def
/FontBBox{-55 -420 2343 920}readonly def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMMI12
%!PS-AdobeFont-1.1: CMMI12 1.100
%%CreationDate: 1996 Jul 27 08:57:55
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI12) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI12 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 12 /beta put
dup 14 /delta put
dup 15 /epsilon1 put
dup 22 /mu put
dup 23 /nu put
dup 58 /period put
dup 59 /comma put
dup 60 /less put
dup 61 /slash put
dup 62 /greater put
dup 64 /partialdiff put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 69 /E put
dup 70 /F put
dup 71 /G put
dup 72 /H put
dup 75 /K put
dup 79 /O put
dup 80 /P put
dup 81 /Q put
dup 83 /S put
dup 84 /T put
dup 85 /U put
dup 88 /X put
dup 89 /Y put
dup 90 /Z put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 105 /i put
dup 106 /j put
dup 107 /k put
dup 108 /l put
dup 110 /n put
dup 112 /p put
dup 113 /q put
dup 114 /r put
dup 116 /t put
dup 117 /u put
dup 120 /x put
dup 121 /y put
dup 122 /z put
readonly def
/FontBBox{-30 -250 1026 750}readonly def
currentdict end
currentfile eexec
D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE
3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B
532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470
B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B
986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE
D919C2DDD26BDC0D99398B9F4D03D6A8F05B47AF95EF28A9C561DBDC98C47CF5
5250011D19E9366EB6FD153D3A100CAA6212E3D5D93990737F8D326D347B7EDC
4391C9DF440285B8FC159D0E98D4258FC57892DCC57F7903449E07914FBE9E67
3C15C2153C061EB541F66C11E7EE77D5D77C0B11E1AC55101DA976CCACAB6993
EED1406FBB7FF30EAC9E90B90B2AF4EC7C273CA32F11A5C1426FF641B4A2FB2F
4E68635C93DB835737567FAF8471CBC05078DCD4E40E25A2F4E5AF46C234CF59
2A1CE8F39E1BA1B2A594355637E474167EAD4D97D51AF0A899B44387E1FD933A
323AFDA6BA740534A510B4705C0A15647AFBF3E53A82BF320DD96753639BE49C
2F79A1988863EF977B800C9DB5B42039C23EB86953713F730E03EA22FF7BB2C1
D97D33FD77B1BDCC2A60B12CF7805CFC90C5B914C0F30A673DF9587F93E47CEA
5932DD1930560C4F0D97547BCD805D6D854455B13A4D7382A22F562D7C55041F
0FD294BDAA1834820F894265A667E5C97D95FF152531EF97258F56374502865D
A1E7C0C5FB7C6FB7D3C43FEB3431095A59FBF6F61CEC6D6DEE09F4EB0FD70D77
2A8B0A4984C6120293F6B947944BE23259F6EB64303D627353163B6505FC8A60
00681F7A3968B6CBB49E0420A691258F5E7B07B417157803FCBE9B9FB1F80FD8
CA0A265B570BA294792DD2FC75CE2C83DCC225B902551DBD11E687EAC6E85D2B
02C28359A40AE66A6A6A8862CB17815B41E280313F0EFAA9981755611F7F683D
35603984D60BB0C772054355A97A5E03C689E23B04DA79080CE4579CC90EF38B
1A64CDD92B907AE83192C3C46C5FC40BB412F6656DC6349E6D29B5936DCE94CB
98E3B465FFF7574095F57BB3750F1A525FDE28FB8FCA4F0DBD8BF16A3F1FD9A9
CD52473E23A90E6632D39EBD39223004B2382EA7B1CE8E90BE77C69CB5B9F659
009CF2105EBACE0CF9BA0295F1937CDBF7F718B6B85C984490D1E560E9989B89
D7905696D5F64BFA604C5A93CA60A8C5C4A5AACDB6EF5562BF55E551CC048835
68743F501BB40ADB8DEC07D5975369A068EA7D38726509F04A997BE221EB4585
0FB2028F907EBEBE3FA13188BCC5DC000765FEC6495BBD687DB29985A7BA9571
C0C192E1B320DB0FBFDC766A7324B7C95A560BD01C155439EB43D1A04065294B
46A4DFAA157D2569CF91936714A6AEE5697501FE521279CFF261C7D433B2ABE2
9D96E5720E9ED02B59CA2CC3D01782E74D45DD4CCD6B47CD7AB46DA29932246F
25C7EB68DE604375D3D9AB22AF9B88E1494C26EE00675BA045A8D89AC58B7720
0A09C675E4537957B8A5CD32D55AA3E61DCAE5E57A9D3AD3DED4F1EB8164C3FD
4E828D323882FB90B91DE0892143A3166E884EE61ECD4D914A71C3EB53237BC7
A0DDBB0CE472E458F67E9E05B433EADCB28F65FD2288E0DDF8F8A970305EEA10
3344ED8858C8FC0E664FA67E5F8A3ED0B625465AFC9054C643E2916B8FA03FD9
7B24AF5D4CE0DAB93E22698328AB963DF7E48F2110AE95CBDFF705F46A091A3B
140D699617AF3DE5BB444845CA815B0FD701A99D04C80B009298C245A3D0ACE7
8C0108D4063E1E473CA798FA77F19A8C689B26E4E452C112D7814B6138622FB3
3EAACDD103ADF9021EE5AE710302645B9300777A6B882F96B951F92E5D4E51D5
32F29BCDCBD70D7F89D4C5CCDF51FD3EFA51EB98026EFC023B22100C42969589
0626B5C9CB7934B5B066141C8B5DA393DDE17C782891C2297D5B212A31723679
3B4930B2DFDB4E6C7F70B76CB486438D247D010DEC30B70922247DF3ACDA0C9A
E8257B587A0C442668712BAC81FB583922E59F856BD5079BF5ACF967D56AB69C
6D05B8B2FF5BFCEA19E442C5959E6F050A3534007D48D4EF192A5A6B6FCFEECA
56F429148A1A7CB78C0BF0C613EA730FED10FD65BCB39A1B4B51251BF31F8D6E
C6488B530394DEAD0A6BAC4C6AB5C9FC01A6EDDFB1853DFC2616EEC7AAE65999
AA539261755C78418279CB23C01EBA963442E8E8336E40BD802E8C8DEB882A66
3B485E9A6FE169CFE7EE824D4AF39C34BC295B42D1DB583AB48EF8BEF206E2DB
024DD2A4E4908581847A5036E615DC75661A2CAF46A71D59716D2829E7C0D1A5
6567562BDDB8A2ACD85D0DE7B5C7F4FA0E20F69E95B6399B2E4CE1C3F381C4D2
F6EB7236175362E4AF41D8A6087841ADC53B8D3180ACA69F940A7A816E3B2BFF
1039DF6B62B4C42B8F95593C29F3776F8CB414ED2E49552592BE86F739E22D7D
C50A9B45916881C2F649A2073EACD3F4D405B2836218D46DB6048BD57804CBF7
8E8EFE7655EA4CD86FDB63748690F7506E41A0CE61108C9161AD25B7F632E511
38E20959BC107BD7B61140169910AF40ECC509A07A1FE0C14F2EA0E354975750
DC6CBF72515280396A3A13D6E8770BA39B3DD400DD9BDA2A3397DF3FE78E0A37
24008AFEADE1DABD19C94DFDE32B7DA98B832AA5892672A51B0D87D645D5FF3D
6038493ACAE295DC907530167B0C9AD7B3959BA7B4BCF931008E939042D9D593
C4C7F606821F3A7ADA2828E5AFCB3CB2B08633438305436FB12D9D5E0B9DF550
F36017F63A9655261F96719861B5B82D23E42C68006C800880775DBA6DD41ECC
89F568E63FF2D0F758918333321B1DD1D98A1A5DDF2EAD79A6F5C83A8BC7A3A2
D3C7B1D0A1EB4F8F7B212C87C5A39C7B31F6D1825FC910CE16E7014B6E2CFFCA
F4C59CFC97AA8E7BF4E5905053E204574469F7E36B429955127C4037E6543039
143DE775B981B52F91F0F5EB1DCC1297005DC3A8874A74AE0790214CABFD0A47
FCBB326E713630773FB69ACFDC3119276289D10055D7CFB8722CBE749743B690
03C45BD5721B16E17D952A5C3025C62E54BD7F9BA0595B74299FA0DB930A999D
4AAF624CC2F813D79340DFEEF261EFE3DE79FBF24C2C037CB6A11A3DD259F703
77F8DEFFD1E2CB694FB669FAC3C0D147CAF4E33696490D5A6320B514FF36DBB4
75EF6716C29D6E888BB5F81CD161F88D0F49C7CDFDF820C74D3F15A923174755
28C7D96C8CB4D2D814505BEF02B894712046464D6B20A6887EFB4AB40E948CD5
E7389E4461833A81A34C0C6C2D3B0C741C25AEF9238D7AC36FAE74927726AAF8
7FDEA5BFB51C83CD3D75825ABE647E26F4283BC84066DDA0270F30EF46632E37
D48A3595B24BBEB700481359B36DCBF3D458F659741CFAEE36004C9AE421D713
41ABC8CFE905BC837DAC83F6B0D2FEF11D6FEAAD6ED7F1454A507987DE24A0C2
867109909B34F922A0DA4C04BA09EABB9E4B86DB0310C642E2ECFF5487DE62C7
2E9D95AA5BFACBD4868DC60E976300D4E29499C23CB9DEA855816E115BE52762
4DEFE59202FE368BD8E87DC7D37E30A703281D50CC3B30AB268A27BB4B1808B6
9C1E9CF57903F980DB5B6BD766E43F9DB257DE9F89AC9C2BB4E2F3C5BCBC4331
931CFCAF55CBDCD03D770661205C517F30F03191680F9F38A5F2E0D130BC54A1
0A12E48FD72F99B0963729798F3AEFBE3973980D956116522CE976284FB40574
8119941B6B218D8252AA458F7EEC9724835B43E53FA931498648C62FB3BEEB45
88D1A7D402CBD6555E8AC28693DB4EF7D6FDE77A232485CFD47E13EAEFBBFE9E
50331D7FD61402338C722D4F71522F66D3E90B47F3E14FFE1F25A6299AA1B3D2
64C2C51CC988E8ACCB2316A3DA415848D3263F59ADFC9DA03CE00E8961F05D3C
D06EDCD69EFC0A65DB4A0F0BBCCB706E860C60DEA868101B2C23B239564D25DB
D87B88A6B61FE9480C32294205A51C2B66192F601F532C4E2354401B109F84C8
E715B992380A7108EE92D910B135E0C3FB47C8E5893EC9F83374F097A9AC1B25
4DCB7A19C1B8A692F2C5DBF195A6D5534078463238BAB91FA94E6562BCA5DCF3
6EDB70B5D677A3FA101AFBBC41E7420548834307B3BCB0FFDA6D28DF94CFB7FC
5A53A630C21C798C79264AFCF1A8588DF5F7D11FC46DEFA867029F46D8B825D4
43983B9EA3969723E03C364EAB7D30BB5C05A8E7DD765A0A85EB9C12781C4B0E
0E46092DFBD963DD21C335570C8649D1DC414D76825BD98DE7728CDF7440EA5B
942401D64D0579F542582801602F4585BF17E2E750087A99ED28B7D7F86267AD
0152C9D0CD0EAA2725D1581F6A3FE8A63FC8C1B1BD3A4E3D918674F16092DFE1
27DF64C1AE7617527E2FF1EE9D4F9FF46AEA41ACE5A00C01B6CFB98D5CCB051A
1355C071908C4E39D5ED52BF68A94829F8820CCDB0C47A7F5F2BBC015CB986F1
F753D985A2285EF1B8AA771AD33EDD2F68B32D4DCB85B69B02AC514DEC808CA4
6A5F4F10954D0F9243847C026A438E9F662F02A655DDABDE764448A2D6724061
537BC2597BAE592724B0D8D397BCD653755CD6001289FEE89B2A3CE794776B60
7AA679DA466822AB1AE9334A41DA0099117B95E4236A2DE9D2B8ACC8C9F5D0FC
E33A3A75AAF03756DB422368C6EE23133A3D448F04FE830424A8CCFCF72C4D29
34D4CC8439632A86E32B5595FCA3C33AC0B3680E44FAD0B7AB0CC0489B873D7A
9CCA2602D61FDB9C4B540027420B3DC4A9DF75CA9A030AB1ECF320FB5E153405
C9A2EE59F636EA568E8E5CCBB9ED7D192CDD8D515E5BEC1A4B7B5571DC9F15C4
4B3B7E351F9BF6F450A66FF88F657F5590A32A67A772291F7B6236F174771609
66747A5472C828ACBA99E040BD512403E500621DC0F6BB24ED41BD64E5E1C804
F100E907BF31A7BB6C97BACBF5C23F3F3B47A25BD3FCA66C2C0DEBF9155CDA15
89D68B95DD6204705468D56D5B4D08451DC9626020745B045B6191A31635597D
6C3AE4F20F64A3EAD68B3F67B4458EA448E5D3352B0D1A054193C82216B9C700
C50FFD1EC34BE37B85D56D8C7D0D0074728CC50D7BFBA864730D7C306FD7083E
F218302E10372ED81ACC5F8224B3C713DAE0534D741C0517B70E43CDB8ABB29F
EE8F4850CA74D1D955364FB91E55FC9330654217AD4529DECCDA9A21C4A60BCF
A13EC1F6BDD72DF9CE1257F030BC7B91C53AA07462246DC5CC832E2A26E92386
056C5094476A6C667AA92D15966C431FB1085A906CD7D684EE1DAFA39CFFF26E
7DF42BC673C12A0154A3C60906DB8C3FF60AA2033F544D9BCFECD5E07F6BBEAF
469B440D972A3AD2C84C64C1F4E329D2C93F3FA88ECD8DE37F6C5F557185B231
B119631E29A0EFB49906765B2367C256945217247ACD16FD45429D85BA32E1CB
696F07EEE81F2811FE641353A74931632D4843E572A57B5E34A4FB4D4C26AD12
D5220E7AD71161B9F6C7B85D32CCD89CAFE30D0AAC4AABAD4087F5AC26350072
9A1E8FF5368CCE37F9C1B191D775C784DC82D3C6A13A8D9C0173D1569CE7D3EF
162981A911146259CD4BEB88D60160D4B453D8420A390FA988A3148E6C9BB72A
BCDD1320FA46D51DBCAB5B34E33C193C25C8875BF3409BDB3B574DE54F1D1F4E
B6FC605EE5438963C3B7989DD8FEC30597E5B2F750A0BE834FA934F5730605AA
4A323C1A74B02F29E81F2B3CAFAE9F99107C77DBA943CFB1A456440E555109A9
AD9C533D31F3F39C8243D6CCBDA69A5D6B2AE6DE17C18C0D0E59F7531157FD13
EF756EA6471DEE6FFE279581CD1B068D15FA76EC6D142E873B6AD270AAF84C86
7BA52079A8D08C413DA165BCBD5FEE92633DB63270D73011799537FEAD7A72C2
689A4646BD833B2F6D9BB6AC1CB5108D0E0AA1EF185B57816540E320D8DE5DF9
E52BB0B0843966C90EEC82D54E2F1AAE4B1574016214A749EE9BD520ADC73748
BC3458EE5BB6B05F4E5CD60DBFB033BF3B450001BD1C2DA300F7DD27AE280E27
A736C68E789AD33B7D2600575A70AD91E5C6D7492A8A4128E91BA83150EC076C
90AC2D8151D209ACA46369ECDEA52A6CF9E750C72A4D6EEFF0EA85E51C56B3C4
F12995744975CBC3FEAA03FC52218794B92ECBD461E751E3923E7EB9832B3D6C
2F6D64305A8CBACE83B50999008BC1B82D22991E87A24ABCEB1ED67DC13ADA69
33B6558D4C4357CB871F5AFF1EF6143E20B87A5C0A996A4B4DB6C32ED653F9B5
BFC799A8E859048CC95051A7E93CBEE366631534A6A75B884EECE78BACEBF2F2
D57CDAD292001A673ECF1AF52136456D77B0C9F8AC1185F3274BA3D3D71F7791
5572578BB280459F0A09D7870E1C8B4E066266638FBF3F72EB5036C998D5A219
CFCEEC315C0212CFC45B2C910B390E5EFF8634BED3C90CA06298B2AF061E63D8
7F6ECB7414616C458260450CE1584053F6845DEB92378D8BC012D1E14C563F5B
6D05DA66CE904FDAE48838D79B8FF691E0C52D7B11D67CB95D045FFB7F57904A
57A0262FF0FF65D801835D468B9F61CE9565B9B46EBC0F94EFAB0BC055A3DF2F
3DB0087BFA82A894BFA7BFD20C0ABF94983E397A03C7D9CDBDCBB6B7894F38EE
37161E1C8E54E1C313E0F294B948AF9400F7DFCE35C871810C333186BC731CDD
8460AFEBE9C1D1512281F1528928514949604A549B2C98C8326C4934E93E3AEC
2420DF3765FDFE7B3E94D736D84EC48A1D28F3CEE7B096D42CCDB28173FEC0FE
13101AE026FE763A727D58541DEF11C0149A9E7E0D7C25AFF61760310B94354C
6AF6E21D06D4EE49677B0492CCB0747F9E0A96DD4AFE1A3CFCDCB4358EBE6099
8F13925065BED267B1F07F5A16F8DF4104C369347C32FC1B136897CCE9F0FA8A
4D7B1182AE3C226843505ACF58BED9F413F2E8A1B8C505CE2F6D458D77F3512E
74BAEED40826FC1E1E114D2FD283BE97FCD8ECC29245B0223AFA4FC4083461B2
89065B56B26DCD1D8B51883A6B603ADD5304277695E378258911AE584BDBD681
B7DFC48D7125860AE117DC3DEA7A5A52D9D616ADAB8CFEE8CCCA117B4CA8EBC3
9F8513D6D0789017ECE8304B7C1D32E446EB600F8B9E3DBF7872C2F64276B67D
1050D91325AB78B808FAE4FA9BA6C03250713B5BA823204CFEC8963A68850F3E
9029727B3A5AEB48CA932A8C201162657E59527D65869D74A0B7870491DD06E5
D2C5A39CF209DCBB2835D359D2B3C91917902257306F36B94FF0C4E40FFBAA09
AC533F723B9E4A2C2C7D1EF6870C79B4DED0F3251A6E27E95DAD6FD7EDFD4CCD
FD2779865B35603B4458DD3679EAF858DD76B9D836C6753606E81B66FD48E25B
43A487ED95EF59AD9777475A31327CBB1B1E92812F3D5D3B7123CD662AB7D780
EF8B784E54D66FDE6104F68A297659D2E2B158898E5997D26E3442B52A8E87C3
33807CD6AF20F399DC89B38ACAED8ADF0C2DE1187855282AAE637E5CD3041F1C
2F237515C33424F711A9896237E17F762538EBBB80BB7E5C6027E5A8638B94F4
9CD0BA33865552D33C8E8D6D761662EA96EABABF3A136D81C0B4A76F994528B9
48C0014839ED0CD16E817EED4DAAFAA8B796D8517E5242E4118EB2079F7E7E97
36F7A55A8E74CEFEAE475908C740A4677374E9DDB38CACF4B2C95F7C17AE059C
59ED411C106A776B0BCE543049FD55BD881DED15692A0BE358E75F2AE6D751E7
74990F92D8339BC320C460D5030892DC3D5503BCEA896F2EF5D55421A9FB916B
C6FCC432694DF0A9EBEF0CD88E672EC6F1597DFF66578FA451D446DCCF2216C6
23606B568D4591749F98C6DDEBEC9BB492DCFDC30E24CF09B4A3D436469B3415
37FC98DBAF4FFAE74BB274F87F2F8D9C334BC58F550608AB3C8B1BC5032B755E
477DF2488943B4C62F29B1714EB6A197907961ECCE2BD0B53859388585F5E2E3
BBF08342C3BD23F61BEFF7380715BAEBEE8861B76A361937F64BDC5356BBBF48
E21BB984E43D05BF22C88EFA4B66EA0E0FBAD961CF7CE75DFBBF457AB1A10E79
383017E1682CB67C6EA1982814010995F619BD38BE3E45AB2B0868707C7758B6
80E969F9F00D7CDDD60C51D03BAA9FFDD20778C8787B6A6B17EF2D1FE755F469
5841004669CF142A4EBA47B73D5D80AA6AC17AE767AF017774AD5615297F1E03
57C31E705BA8F9AE7906884E1EBCFF230B2F954C2AFDF5DE966EE58E174793FD
2BDF3FD5F2CC5C9C44DF58059935695CBDAB6A356235D0E400B2601668DACD34
E523758CED1006369A730F9C3EC8C5C14F912D80B331A3FD9FA0650724D8BC46
60A5467D52B9E81C2EF17E34971B86FC54C4126DCEB4E9D73A1E8606C7E3CEA5
C8850E206E2827FA5F45637AF9907D0E9BDAAA96F9B053C13648A7B2EAA3BECD
4A4774B5A5419655B47BB139F9F440B3300578EE84F366D7123E8D7D73867EA5
A31D3CD9A03C8D16E2525324CADEEE61F1940D6C609FBF23A5A1D341E49889D5
E5635A79507E639EF5410782FCB7219E716B1381524CBBD05EAB0F01521DCB2C
C0760785ACC91CB868C8D4EA17C82D3D978A3D29038C121030C1C390F0E8AD8A
6E99F7175B71A1BEE479183A1EBC55B89F8A3E87EE8136DCB50722DF493CF765
BFB799BB2D36C458501990754469A5576EC8461DAFDC645A0005B67244EE0265
E5A917078051E9FDFE012F9AB11DDED029762838ABFF746CBF6C30DC9D600178
879EF63A1909B3F3342B3B9831C1F23369B3F056A9A20D3583277AABCE27098C
62AD9A7D344733DE4837DF373730A9F80BAD33B974D8BF8C56B8940CA6BEED33
A4F7D211915D8D8081102289357B7A1F7BC76AD24C466F38CCC50A0C4803DFC3
CD87998DE54EF33291F30F9092B138E5FE5C2EDDB0799991DDE7A989CD546333
BFE908E28C78518C00C01ECFF3B35D52D390168C686B8A8FE8A854D50269B787
2E644A22DE1D207934E0814EE0E1B25E6F8FBA268FF34A2AE4B10F040F66707E
52D237C413604CAD685BA336F97EC7CFEFAEF5E4B0E1EE588A151784EFC3CC77
5E7BC5ABD50776BF4379BCAA04D87183A06ECE9745E605A2558F1CAE5D083F3A
C71D25BCF55728EE99E83E1F669585277A4FF53204CEB6081BF5E99E0AE814C7
BD4F10843D4ACD859AABEB39109B0E253DA322BAE866EEB4D3DF92ECCA7947BF
ECF484E90A2481893B8CD428B8B323AEC52F04E1BB36B05ADAC4A40B2D8B2CE4
5044C2072B4273161F746D4B0FF11929CAB07D2AAB6214DE33F77B9B1C38BB48
32C107C1D7EE4A2DDEFB264FA932C33C07D3582B2F47A47C8C691BC9D69B419A
315EEFD28055C829034B227D71EE99FF4F5CADBBB565CA69431423CA95843021
174CE443D1633DCC3E887F8DB6C8D1A8BBA9C516F17557AE838D2A6CE5F5C557
1E310282720FD8543C92946ECC15EC1F674C351D3E78E2FAF8C49721D1B364C8
65FAFE6D2E529BC615D0B346A1B35DC646245799D6B67A897B8B41BEF8EB3F52
B636DCDB0666D9F76B3AF060F39C39B88E0768E7124511803311B96F79F177FB
9611C78DD9C4BA15315EDC3622ED646775DC5435FC0E07852B205A1745D24236
A7D9443CDF0F87BEE00684AAE76A7E0CF57A9CC73FE0F687D53EAD73213CBF49
B70278CDC6101DA00706634BFBF1390DCB1A5289C24F9B3C6335AACE5625CC83
6A9179E7ACE27EC0E5006F4FF2CC529D8238B42BC891D00284BC1519E9DA3B6C
92D56E37B3EEC048BFC4428CEBBDC76A417B10D936981221EC7CEF4379E714FF
F3781AA2E2F19079E653269B05C60FA96ED4B0E1885B7396BE4252A6577E2C91
557711EAA3B269F7AC1E67EDF260156C3F6579E87EEB5B8EBAED73F199CAC22E
381DF965ABD9FBC19D8FEB779B21F07E58AD2B6A727B34FEB0B2F46CF9655D30
A9E5EC591AC591B413B21C1CE43341C6B7E9E168085831BF0E0BCA0130D50817
156C6ED9966FC858D8BB11258FC8215E0EFB480BA4A8921B9AB4D7334D1D2250
6DEB27E536BD0A87B4084B913225D849AE0FBAE2F094AE98AE46C2C20E8C6912
22794BEEA788910B06C9AE41107A89A591B89446B1B813BDB141FB4B7C4F630C
5F9D07E6343209FA05A449986DA33DE55DDB4B325521D7F10F6CCC0647663DE7
A4CFF9F13BEFB9A43373FE7BC1E6C71FE2A253ACBF6308545835EC1499FDCFEC
1473138DA61F3D11D635AE5AD5CDB7098537D484E75785752F1C7743B236459E
D035908B330E48DBD4BD588E5F2F3D9C06A5CC63081C9ABB899E339A81F12F84
564358A5EC636A221CA6E06AB4E34A07222767509DDA4AA6E856C58AB6C42A34
E33F82D28B557B380793B31B42DA7307492CCFBD87374AB9AF8372F11043E2B9
6E66AA41D1CC4AE30B67779B200F9860B6704EF95DD2FB52075B24BF05E912D9
B3B669F81F85FF5189823DB61509CDDBFDEAE2F14AB334F6C105F90DA4B21A93
1841C3495908200D6547EE01610E75799EEC22B4A5A81B090E851CE88CAC397D
922EAA194ECA14C7399903325221E04981DC1273580D6E7DFB97D85917B1391C
50CD6EF357EEF6D1CF9189DDD67B213AEC1C228B675E132F93AC4389BF5B2FCC
EB6C989D641E1E6DD2671283EE0F50A643C2FBF9AD7822086B1F8151DA5166B2
6E445AF99223C8AB029329E541DBAA1848A8FA4FC2753DF4BCEDB8EAB44CBB4C
D7EA275D5E1D9F06780A84FD605462C73F84D1FC44B734B6C91FB4B827A6CE19
583932E2EB422F2E364C91CD90730D39D52CA7C7A68095F58288A38049DEC801
EF72EFD072E8A3E05CBCC7A85ACDC0959413A274529379E1B76996E1F871B0E3
34A0C52B1AAD03A8234849CF414FCDEBBF458C23CF1591388E42AD9DD24CDDD7
C57496F62C0E2764950EFEAB7C3ADD93D78349D370AB1FA3373FD96AE22EEB5F
E93F064250314107501F4E56B358426C2FC62C3C557FC626074CC6B20C8792FB
CA222B6EE70850A1E55EEB648AF94B7D4B979A6055F3A5791A56AA9EE23CE013
3DE3D0FB1C6F368E20AFAC8023B11FB84F57BA3F7DDFBB13031326C89F612482
A257654ACA96312EB2C45E0883A81798013FCE5F8889282907DD84727343A7E5
AA97EE753746DDF5291BB2A9174C2F1B2BF82BAC10414079EBB14640CAC85B48
1BB35FE8A6701A280EF66CBE24031AA2FBE292526F4F4C0D4096D0EEEF113644
8827B7E5F266A2ECA80EAEF25E25898A49974B6B605972E750E6704FDA994F13
8CFA0E695478E67C012B94C6AEBA9A91D6D120B6B564B05BCA5BD3809853D6F3
2037E0F08CEA7D1B73715241D58832503B709A16C9D8C60DDB0FA1C43D722B4A
520E07D02AB581094C9599BAB63DCC3EC182D50982D7B592A7DB4E6BD009E86D
E7CA2134F15C98FED13DCA94517BFFBF04EC664B68DA89ACA5CB6C4B56BB4CBE
9A67CD2425CA14AD0DC5919807DE4165B3E8D444AD06742CDCA7166E8C118F8E
33D415C483CC078A13E0DB646D613872EC0A92F3F0AEBBC58A4D389AD36834EE
43DD73D5E4D3C5E42D837B11DDC82FAF183CC256BEE522F86A5A86C2C27A7757
AE2F80D256DE22765623D7451FBB3DCD83B78F053290D6B2E5EFBFDD4392A02D
17437975ED78A2883669CF552D7DE4CA1ED529264EE490B20CBED995559707B6
2D9C5AAB7C75303BC3001DAE5153886CAE648C2579AB4E6FC9B121F7EA6992E1
32BBA74A38181A73754A70016C3F6629B6158E496AA72F399733F3190ED4DCD6
31B7212537A181FAF07C1E31ABE18B939FD87137ED8617CDB793D19B06375EE8
37E83DE183DDAA8428694F866D79BC85A1512B40E738D78C2C381CB9079A2138
AE39627E77AA7A3487F21F26BCD01F92A8CCBCCDA75A483BC8152CCB14D7185C
B2767019F508C973ACB82A29C4E47693DD9FA36CF6295381465215448E965D49
88825C8EF1BD26B821465D12FB1566547BF1CEAB8D7C64D9725E43EA8D12D8E6
D3A7B117C44FB29F183EFF442F1CCB45F769128D77F9BBDF54A89ACA81D0816B
BBA604FCB67F2129F58AFB0B7F2C0003BD55D4065C7DD4F1AC767708122A557B
37C0A933C1AC4D363337EE33D6C109B3ACFFDE2FD418B5ED94F6FCEBDC19C87D
65581B43D4DB9014163D4DDB5AB1261155D105CAC9A7BA39198A7BA8D8F5754D
8AB255B43E20E86DDB3437DD2D2AE73BF500AEF4797A39808D80AECAB3FA072B
F7691F37A5D4318AF9A3243ED0203ABC5AD1DD3D1FCF768770B4EB63007EEE6C
5610271EE7C8BDDFB0A70A9756915781C2733B1E4949ECC90EFA4DB8D807723D
84A035582CABE30D8D6522203ED7E5CCCCA3031442344E059E4901A38DCD4660
28068A5913CF90580ECEE7420E28C27BC99981F0165B5CDD638D30EA798B54EC
D2B5F259135CDF567F9C4A6F79AD9B7208C473B69743F2B1CB2B12D82BCD6543
19282F0A2D1802532671084F17D5E3E7CBF0F282B21935B2FB4AC4AF3D1458D9
769DF07FA14D382F7D40844BC9AFF06A92E33BC05C4353AC2A55AD28270FB78A
1DDEA34850114918BF85FBFA9D03814B9A1DFF3EC3B5A63CA2D12E9FC0F92DB9
7499B7123B7DAC655B425B53A5D3107E16633EBB2A112011D5CA53E2B186D485
DAF322C3FE21DF8A881A87D6419F39EF5F47D18DFE871357F72E06F49E9A791F
DBFA3F93D8B89CF7956187AC1101EF4E3B13BF904E8164A62AAA2AA2C2EA3BE0
C0C91DDA7308258E3ED4F2B4EDCEBBD7DDD6EF74DED605E5AA50EC64F4848346
33579C9AF7959FF14F72E33B5752740771FE237C354AB51719730F4CD38EF14E
CEA42D6BEB30EC87BD987472DA651C9ECA57A0A10CAD69B07D2CE53B7731CFF4
642639D29E20551B0C93E1E6331F75A290B01B4BE9408479FC5DEA406E65BF66
8A6235CCF6AF1A4FBF303A7655858D698EE0685C358E24AC0C88C2DF9E1FC36B
A261F1F20BFC97777AF80F647B79D15EA18C9CC2ACAF31B2661F52FDAFDC6A0A
0147F7E7AB2D7A7377F9276341922E96733D37A2DDBA8DEDF764CBB22360DD29
1C57C6EB26EFF8392E46FA5080152D478EEFD6BBDB1104A936B24823EF752C0E
A7D3A805DCCE734426639506CD596188539F04027555E885D21D5A20A67D77DC
1514A547394B20B2AED38054184C18B09D0741E843BB93E86F7AA1D285E47864
6D1259127584D167650E51237C5872ADE4C00A9FEF13D06A08FD8543D181A7F8
73045A0261B48F2035B3D9BFFD966A1D234D7B55E478395E0C3E9672ABDDA8E6
09CB7EC98E144DE101EE4E39B0FA461B2B7F3A9B13D6CF1D2648949AE6F54D48
B83E2D060D1D3EFFFE89208BFF1B78ABA6D72C8A7B15DFFB98FDC9F86BDC99F7
CEA395365B41EEB70D05C18E166041F83E39AC6F3DD711C612136771FC489E34
48F12DEC4E44FFEC16582550AE5B03953D46ABC965C4A93CB3533CCA4000680A
D0C1432469122BC6FB708881086862F0B3112993BE5376F21A5CB10FDD3FD28C
C98125771AF1BFA7BB394687322D543D19C23EB1E50D0E25B187748346C2F5E4
C13618B6F3313D014C77B007C07782D070515C95B2B5BC71CCE9AE0F867626DD
BBF0888178884CB7F30F68A98CC165128043DF8A7A2F3BEB26D470D6F3CEB072
8E12952A994FEE4B269BE93D609926569C60D81696B23083911EA48CF4224378
6BEF40B5C0041371B95999DC2D5AAEB7D87F0605BB771CBAF5CB081F0EBCA1A8
A93D3C2431374717DBD076E8B4185DF74B31B7158275915472CC4B4A7D02FEC5
16C5E27B956C3BEBEC7FA4EBE310657C24D02BA95B99FDFCB9E70FFEC5E5E428
CCC26115F60BD17C39408FDCA405A8285C9175F3B8C6623949A05F8BC3405526
22F4AE8293C2889FAABF30E97A47D91D41D12CF7BF495B2235026BBA5DCA35A4
FCB233C4123A0099480B9638214BE65E01D946126FBEE68A003C4B138954B2F1
522544D8F501B092ADDD76DF4D0AF95E822BA53E51DEF9ACF9BB448D8BBBEAB4
35A69668C722B1DE5734DC3DA8F84C1D544372D2F2EBDC672DE38703A62C7C0E
4BE52E9DEF19A2F2BC481748FC00EB29DFCE06CE5B6D2B5AA6D749EBBAEA5A5F
9C703B90A349CE3CCBC1BCDB138E20113ABBC085AFCD94567E04D0F82E00B615
CFF5382A58EB445F286ABC33A6744159F219647F59462E61A4BF47DF32778EE4
ED1876A5F2776891492E8BB7D2C0500348127B1F80252E4A69A6A77B7A445D36
1CF3967BE933B1332CA3583467315341E54CB4383B9361C1EFF8C7698D9C0895
D13F94242AC7022A2B9D304CCB5F93E8E06D53FA8E1D2DC07FFFBEB04533E1C9
DA670D6FBDC3EE9EB90AC65645F825BA0591005D0E660EC15C8A02CADF64A3B7
04F573DE8E496AED9642A9DB69BF7E74C67E8A1327DCC3BBC555D27039D133BE
A4D3C35F75455E5E9A264A18C66E4DED9C9EED6120BA933BF16EC6F275963984
DABF22F7300F3B99F9B5B5759FC79A50E0033CC6CCEF45D22B725FFCD3CBBA37
A38D6A9435082E1EEC12CB9819C3EBB1BFEAE8F4C34D133EA4550D518C092750
5A9571BDFB004DA77506286FB136A075D76AD6A27B1B541DBD337FEF68B1B8BB
EF85BC6CB1E791D4E65C7334B773AFE9EBAFCFE0C91B63CE37279EF8F6B42244
41B8BCF504C1B6231F14E25FB22299941EF724E34F492F45A49589FA9FC2DA1D
BF4362F47D7962C962A5052F7C3B0490974EA97C215A8AB5BE9054E4338C4760
1A0F39B673E05F94968FC9D8FE932077F5481A94F19CCCCE8F34D96A4E497C95
2C3F0E9EF82E84E761DAC0E0AEF7044C7220E34451C9A55B78A4F73FD8FFA844
76D679642C1DFCB869BF6C82DBF8766E9578574BE8EC33959D45C6071A83BB9D
2994AAA1ED3845060DC271A8783C6072B5B0E9D5AC3DD83323BC24E4FA54108D
997895C329639A993D7904E34AA00C39D86E2B6A0A8C0E0B137CE6EF59270DB6
AE3E5B321BD15B1A01D29876391D0735A399259F88E3D5D92B9DEE4F294B9658
588B63AFBDDC1B6C64D187CDBC05D41539B8A6C54FD1CB669357F249AA54C95E
643ED829C5F62A9DE12E526B519B6969C116FA9EAC713E283AAD915C33A9BE87
8D1B9F1C41B3315C2907EC6511885BC785041070D4741D7460C9254E441AF4CE
6A6498A593C580573D140E287DD225243EADF75F91A53BB4187E8C6F184A8ED6
88C784D981400F9AC9918B2AFCBAB0B9177B96BF12BE2A2962007C082DC020B9
6C4837CC743F22F9D4258CA029132527EFA3CF627A723CC9AC48056B56A138F6
E39D1DD6C06C4A93DEA397B23712FEF7EA4E3114A1240625D88B369A145FC2FA
BD995D18EDEE1DDD59A84488D7F974A0FFCD3713BB35E3B4B5109785E99EB983
3F791B00C092CF2B0AD54B1B4446123561C4B5B2EF011927D586F0D0E4F3BDA8
35DDF9D7A789CC70019674A0B58D0472E75321ADFBAECC5B22222021CB8A0366
4722EC02D925BA446D3811DC7353082152F1B4C9C7D323F554C956443E7F1322
DE835E94B21940FFD93FACEA819E73EBAEF3242C2361B55C3991FDD95DEFC69F
1CAE12360F56E0AAD2F41A74A820A07C9334F57A5B878441C87EE8CF3032D463
74524C6904F32D3C65096EC2D4734881AE9BC7E4F6E243A498BA7F1E109E3CED
0BA72F63133FCC959A0D4C28ACE8A961811DA0072BB828EE659D4572AC178A8A
562214273FA319CBCAECFDA51B38199D3DCE1E32CC5D095CB89E6599161C6F9B
E9B0C296BBD8026BE2F7F10733D283104F3C2EC38AB6CCB804A04D7E5666CDC7
203705B80CEAC9B912471385C43D6616D6F6A2923064E01CB6F2AE0A1EDCF1FD
334AD255A34E1B0DFF57A43C1E2B6DDC7AE82014EF3CDC07BD8C21BE359F1693
D4F7D82DACE1396531EF4F57E4B70D9B7BBB3A14C826F44FBA6454527DB4BD12
3D80D2F449EA5FCC755B6E81F52C21702BB162DD46CE899A075BCEED77E7ED66
80E98CCCB116A699732380696914D58A2ABA2BF70CEE1B6C54A412AAB78B2919
15CA0668345051080C907FEECE1B4612E1CE614ABF0910D574C8D41DAC8C71EF
9665F505DB258FF9C407778BBB1978DD040AB2EB4DFDE3084F93F4EDDC6C6A3C
AB469E6023A72F3ED6481521B656717B586A9315827E4ACE3D727ACB5A04DD5B
1343B67099316AF451058D1AC6DD6C40C78C02828D013D681CA5C32EFB277300
3938B742E98B24A7EDB61E62DB53B5F9EDA0CDD2330B51805ADB0ACEB40F7129
0E80609F34764C90B7625FC713CD5EAEFA6D178A73E85431BA765A5BCD00791D
86A8C5E111794326BC51D998621632EDC64F77B0365D9B63B7A7D912D949C72D
4D9AFA7B40394B759916E7833C523507A069609DE0C1B92C565E593E5139E335
DD5D3828489C7E8AD7AAA8693285A9C21A5DE92E2401053A54ADCCCA
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMCSC10
%!PS-AdobeFont-1.1: CMCSC10 1.0
%%CreationDate: 1991 Aug 18 17:46:49
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMCSC10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMCSC10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 19 /acute put
dup 44 /comma put
dup 46 /period put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 53 /five put
dup 56 /eight put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 70 /F put
dup 72 /H put
dup 73 /I put
dup 75 /K put
dup 76 /L put
dup 77 /M put
dup 79 /O put
dup 81 /Q put
dup 82 /R put
dup 83 /S put
dup 85 /U put
dup 87 /W put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 121 /y put
dup 122 /z put
readonly def
/FontBBox{14 -250 1077 750}readonly def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMR12
%!PS-AdobeFont-1.1: CMR12 1.0
%%CreationDate: 1991 Aug 20 16:38:05
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR12) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR12 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 11 /ff put
dup 12 /fi put
dup 13 /fl put
dup 14 /ffi put
dup 19 /acute put
dup 20 /caron put
dup 33 /exclam put
dup 34 /quotedblright put
dup 37 /percent put
dup 39 /quoteright put
dup 40 /parenleft put
dup 41 /parenright put
dup 43 /plus put
dup 44 /comma put
dup 45 /hyphen put
dup 46 /period put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 53 /five put
dup 54 /six put
dup 55 /seven put
dup 56 /eight put
dup 57 /nine put
dup 58 /colon put
dup 59 /semicolon put
dup 61 /equal put
dup 63 /question put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 70 /F put
dup 71 /G put
dup 72 /H put
dup 73 /I put
dup 75 /K put
dup 76 /L put
dup 77 /M put
dup 78 /N put
dup 79 /O put
dup 80 /P put
dup 81 /Q put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 85 /U put
dup 86 /V put
dup 87 /W put
dup 88 /X put
dup 90 /Z put
dup 91 /bracketleft put
dup 92 /quotedblleft put
dup 93 /bracketright put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 106 /j put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 113 /q put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
dup 122 /z put
dup 126 /tilde put
dup 127 /dieresis put
readonly def
/FontBBox{-34 -251 988 750}readonly def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMMI7
%!PS-AdobeFont-1.1: CMMI7 1.100
%%CreationDate: 1996 Jul 23 07:53:53
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI7) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI7 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 100 /d put
readonly def
/FontBBox{0 -250 1171 750}readonly def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMR7
%!PS-AdobeFont-1.1: CMR7 1.0
%%CreationDate: 1991 Aug 20 16:39:21
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR7) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR7 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 43 /plus put
dup 49 /one put
dup 50 /two put
readonly def
/FontBBox{-27 -250 1122 750}readonly def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMMI10
%!PS-AdobeFont-1.1: CMMI10 1.100
%%CreationDate: 1996 Jul 23 07:53:57
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 15 /epsilon1 put
dup 100 /d put
dup 110 /n put
readonly def
/FontBBox{-32 -250 1048 750}readonly def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMR10
%!PS-AdobeFont-1.1: CMR10 1.00B
%%CreationDate: 1992 Feb 19 19:54:52
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.00B) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMR10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR10 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 12 /fi put
dup 19 /acute put
dup 20 /caron put
dup 39 /quoteright put
dup 40 /parenleft put
dup 41 /parenright put
dup 43 /plus put
dup 44 /comma put
dup 45 /hyphen put
dup 46 /period put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 53 /five put
dup 54 /six put
dup 55 /seven put
dup 56 /eight put
dup 57 /nine put
dup 58 /colon put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 70 /F put
dup 71 /G put
dup 72 /H put
dup 73 /I put
dup 74 /J put
dup 75 /K put
dup 76 /L put
dup 77 /M put
dup 78 /N put
dup 79 /O put
dup 80 /P put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 85 /U put
dup 86 /V put
dup 87 /W put
dup 88 /X put
dup 89 /Y put
dup 90 /Z put
dup 91 /bracketleft put
dup 93 /bracketright put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 106 /j put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 120 /x put
dup 121 /y put
dup 122 /z put
dup 123 /endash put
dup 127 /dieresis put
readonly def
/FontBBox{-251 -250 1009 969}readonly def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
%%BeginFont: CMBX12
%!PS-AdobeFont-1.1: CMBX12 1.0
%%CreationDate: 1991 Aug 20 16:34:54
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.0) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMBX12) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Bold) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMBX12 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
/Encoding 256 array
0 1 255 {1 index exch /.notdef put} for
dup 12 /fi put
dup 45 /hyphen put
dup 46 /period put
dup 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 52 /four put
dup 53 /five put
dup 54 /six put
dup 57 /nine put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 68 /D put
dup 69 /E put
dup 70 /F put
dup 72 /H put
dup 73 /I put
dup 76 /L put
dup 77 /M put
dup 79 /O put
dup 80 /P put
dup 81 /Q put
dup 82 /R put
dup 83 /S put
dup 84 /T put
dup 85 /U put
dup 86 /V put
dup 97 /a put
dup 99 /c put
dup 100 /d put
dup 101 /e put
dup 102 /f put
dup 103 /g put
dup 104 /h put
dup 105 /i put
dup 106 /j put
dup 107 /k put
dup 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 112 /p put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
dup 118 /v put
dup 119 /w put
dup 121 /y put
readonly def
/FontBBox{-53 -251 1139 750}readonly def
currentdict end
currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000
cleartomark
%%EndFont 
TeXDict begin 39139632 55387786 1000 600 600 () @start
/Fa 152[42 42 102[{}2 83.022 /CMSY10 rf /Fb 133[44 44
3[44 44 44 44 1[44 44 44 44 44 44 2[44 44 1[44 44 44
44 44 17[44 11[44 2[44 10[44 44 44 44 44 44 44 44 1[44
44[{}31 83.022 /CMTT10 rf /Fc 199[48 48 48 1[48 1[48
48 48 48[{}7 83.022 /CMBX10 rf /Fd 173[48 82[{}1 66.4176
/MSBM7 rf /Fe 255[48{}1 49.8132 /CMSY6 rf /Ff 252[77
3[{}1 99.6264 /MSAM10 rf /Fg 204[30 30 1[30 4[47 43[{}4
49.8132 /CMR6 rf /Fh 172[45 83[{}1 66.4176 /CMBX8 rf
/Fi 155[32 100[{}1 49.8132 /CMMI6 rf /Fj 152[35 35 10[47
38[63 1[47 1[19 47[55{}7 66.4176 /CMSY8 rf /Fk 175[105
56[58 58 2[73 73 16[46 46{}7 99.6264 /CMEX10 rf /Fl 165[47
58 3[58 55 43 57 1[52 60 58 70 48 60 1[28 58 60 50 52
59 55 1[58 7[38 38 38 38 38 38 38 38 38 38 3[21 24[38
19[{}32 74.7198 /CMR9 rf /Fm 128[42 4[34 40 39 55 38
45 28 34 35 38 42 42 47 68 21 38 25 25 42 38 25 38 42
38 38 42 12[59 47 1[64 56 64 1[74 3[32 1[64 1[56 63 59
1[62 18[25 30 25 4[25 19[42 6[47 12[{}45 83.022 /CMTI10
rf /Fn 143[83 1[50 3[28 2[50 50 9[66 66 31[50 8[66 20[100
2[77 4[77 77 1[77 3[50 12[28 77{}17 99.6264 /CMSY10 rf
/Fo 138[39 27 28 28 1[39 35 39 1[20 2[20 39 35 1[31 1[31
1[35 16[48 12[51 5[55 5[35 2[35 35 35 35 35 4[55 1[27
27 27[39 12[{}27 66.4176 /CMR8 rf /Fp 133[40 47 45 65
45 52 32 40 41 45 50 50 55 80 25 45 1[30 50 45 30 45
50 45 45 50 12[70 1[71 1[66 6[38 1[75 64 2[70 8[30 8[50
2[30 35 30 29[86 1[55 12[{}39 99.6264 /CMTI12 rf /Fq
141[32 1[36 1[43 4[24 4[36 16[43 53 10[55 11[20 59[{}9
66.4176 /CMMI8 rf /Fr 172[55 72 15[66 66[{}3 99.6264
/MSBM10 rf /Fs 133[45 48 55 2[56 35 1[44 43 49 1[58 1[29
51 40 33 1[47 48 45 51 42 41 51 6[67 57 81 2[66 57 60
1[77 63 75 3[83 2[81 77 63 72 1[70 74 73 51 1[76 49 76
27 27 34[48 59 6[39 43 1[55 12[{}48 99.6264 /CMMI12 rf
/Ft 134[61 1[83 61 61 59 46 60 1[56 63 61 74 51 63 1[30
61 64 53 56 62 59 1[61 14[80 84 1[84 5[40 2[71 1[83 78
77 81 11[55 55 55 55 55 2[32 26[55 19[{}37 99.6264 /CMCSC10
rf /Fu 128[49 49 3[43 51 51 70 51 54 38 38 38 51 54 49
54 81 27 51 30 27 54 49 30 43 54 43 54 49 3[27 49 27
60 1[73 100 73 73 70 54 72 76 66 76 73 89 61 76 1[35
73 77 64 66 75 70 69 73 1[46 1[76 1[27 27 49 49 49 49
49 49 49 49 49 49 1[27 33 27 76 1[38 38 27 1[81 2[49
27 12[49 49 4[81 54 54 57 11[{}85 99.6264 /CMR12 rf /Fv
155[35 100[{}1 58.1154 /CMMI7 rf /Fw 205[33 33 5[51 43[{}3
58.1154 /CMR7 rf /Fx 145[50 9[43 84[34 15[{}3 83.022
/CMMI10 rf /Fy 133[42 51 1[69 51 51 49 38 50 1[46 53
51 62 43 2[25 1[53 44 46 52 49 48 51 9[92 1[68 1[51 3[70
1[82 57 70 2[68 1[59 62 69 65 1[68 8[46 3[46 1[46 46
46 1[27 1[27 44[{}41 83.022 /CMCSC10 rf /Fz 128[42 3[42
37 44 44 60 44 46 32 33 33 1[46 42 46 69 23 44 25 23
46 42 25 37 46 37 46 42 3[23 1[23 51 62 62 85 62 62 60
46 61 1[57 65 62 76 52 65 43 30 62 65 54 57 63 60 59
62 6[23 42 42 42 42 42 42 42 42 42 42 1[23 28 23 65 1[32
32 23 18[42 42 6[46 12[{}75 83.022 /CMR10 rf /FA 134[59
1[81 59 62 44 44 46 1[62 56 62 93 31 59 34 31 62 56 34
51 62 50 1[54 10[85 86 78 62 84 84 77 84 1[106 67 2[42
88 1[70 74 86 81 80 85 7[56 2[56 56 56 56 56 56 56 1[31
37 32[62 12[{}51 99.6264 /CMBX12 rf end
%%EndProlog
%%BeginSetup
%%Feature: *Resolution 600dpi
TeXDict begin
%%BeginPaperSize: a4
a4
%%EndPaperSize
 end
%%EndSetup
%%Page: 1 1
TeXDict begin 1 0 bop 1010 540 a FA(COLOURFUL)50 b(SIMPLICIAL)e(DEPTH)
462 789 y Fz(ANTOINE)28 b(DEZA,)f(SUI)h(HUANG,)h(T)-7
b(AMON)28 b(STEPHEN)f(AND)i(T)-7 b(AM)2893 768 y(\023)2883
789 y(AS)28 b(TERLAKY)299 1224 y Fy(Abstra)n(ct.)41 b
Fz(Inspired)c(b)n(y)g(B\023)-42 b(ar\023)g(an)n(y's)36
b(colourful)h(Carath)n(\023)-39 b(eo)r(dory)34 b(theorem)j([B\023)-42
b(ar82)n(],)40 b(w)n(e)e(in)n(tro)r(duce)299 1324 y(a)g(colourful)g
(generalization)e(of)j(Liu's)f(simplicial)g(depth)h([Liu90].)69
b(W)-7 b(e)39 b(pro)n(v)n(e)e(a)h(parit)n(y)f(prop)r(ert)n(y)299
1424 y(and)g(conjecture)f(that)h(the)h(minim)n(um)f(colourful)g
(simplicial)f(depth)i(of)f(an)n(y)f(core)g(p)r(oin)n(t)h(in)g(an)n(y)f
Fx(d)p Fz(-)299 1523 y(dimensional)28 b(con\014guration)g(is)g
Fx(d)1389 1493 y Fw(2)1446 1523 y Fz(+)19 b(1)28 b(and)h(that)g(the)h
(maxim)n(um)e(is)h Fx(d)2605 1493 y Fv(d)p Fw(+1)2747
1523 y Fz(+)19 b(1.)41 b(W)-7 b(e)29 b(exhibit)g(con\014g-)299
1623 y(urations)g(attaining)h(eac)n(h)f(of)h(these)g(depths,)h(and)f
(apply)g(our)f(results)h(to)g(the)g(problem)g(of)g(b)r(ounding)299
1723 y(mono)r(c)n(hrome)c(\(non-colourful\))h(simplicial)g(depth.)1549
1979 y Fu(1.)49 b Ft(Intr)n(oduction)100 2153 y Fu(In)26
b(statistics)h(there)g(are)f(sev)m(eral)i(measures)f(of)f(the)g(depth)h
(of)f(a)f(p)s(oin)m(t)h Fs(p)g Fu(in)g Fr(R)2957 2117
y Fq(d)3024 2153 y Fu(relativ)m(e)h(to)e(a)h(\014xed)h(set)0
2270 y Fs(S)34 b Fu(of)28 b(sample)h(p)s(oin)m(ts.)43
b(Tw)m(o)29 b(recen)m(t)h(surv)m(eys)h(on)d(data)g(depth)h(are)g
([Alo04)o(])g(and)f([FR05)o(],)h(see)h(references)0 2386
y(therein.)63 b(The)39 b(depth)h(measure)g(w)m(e)g(are)e(in)m(terested)
j(in)e(is)g(the)g Fp(simplicial)g(depth)g Fu(of)f Fs(p)p
Fu(,)i(whic)m(h)g(is)g(the)0 2502 y(n)m(um)m(b)s(er)29
b(of)f(simplices)i(generated)f(b)m(y)f(p)s(oin)m(ts)h(in)f
Fs(S)34 b Fu(that)27 b(con)m(tain)i Fs(p)p Fu(.)42 b(A)27
b(p)s(oin)m(t)h(of)g(maxim)m(um)h(simplicial)0 2618 y(depth)39
b(can)g(b)s(e)f(view)m(ed)j(as)d(a)g(t)m(yp)s(e)i(of)d
Fs(d)p Fu(-dimensional)i(median.)62 b(W)-8 b(e)39 b(w)m(ould)g(lik)m(e)
h(to)e(obtain)g(a)g(lo)m(w)m(er)0 2735 y(b)s(ound)33
b(for)f(the)h(depth)g(of)f(simplicial)i(medians.)100
2851 y(T)-8 b(o)27 b(do)g(this,)i(w)m(e)g(consider)g(a)e(generalized)h
(problem)h(where)f(the)g(sample)g(p)s(oin)m(ts)g(are)g(colourful.)42
b(That)0 2967 y(is,)34 b(in)f(dimension)i Fs(d)d Fu(w)m(e)i(consider)h
(sample)f(p)s(oin)m(ts)f(giv)m(en)i(in)e(eac)m(h)h(of)e(at)h(least)g
(\()p Fs(d)22 b Fu(+)h(1\))32 b(colours.)46 b(Then)0
3083 y(w)m(e)31 b(de\014ne)g(the)g Fp(c)-5 b(olourful)32
b(simplicial)f(depth)f Fu(of)f(a)h(p)s(oin)m(t)g Fs(p)g
Fu(relativ)m(e)h(to)f(this)g(sample)h(to)f(b)s(e)g(the)h(n)m(um)m(b)s
(er)0 3200 y(of)e Fp(c)-5 b(olourful)31 b(simplic)-5
b(es)28 b Fu(\(i.e.)i(simplices)i(with)d(one)h(v)m(ertex)h(of)e(eac)m
(h)h(colour\))f(that)g(con)m(tain)h Fs(p)p Fu(.)42 b(W)-8
b(e)30 b(fo)s(cus)0 3316 y(on)g(the)h(situation)g(where)h(the)f(p)s
(oin)m(t)g Fs(p)f Fu(is)i(in)e(the)h(in)m(tersection)i(of)d(the)h(con)m
(v)m(ex)i(h)m(ulls)e(of)g(the)g(individual)0 3432 y(colours,)i(whic)m
(h)h(is)f(called)h(the)f Fp(c)-5 b(or)g(e)32 b Fu(of)g(the)h
(con\014guration.)100 3548 y(If)k Fs(p)g Fu(is)h(a)f(core)g(p)s(oin)m
(t)h(w)m(e)g(w)m(ould)g(t)m(ypically)h(exp)s(ect)g(the)e(simplicial)i
(depth)f(of)f Fs(p)g Fu(to)g(b)s(e)g(more)h(than)0 3664
y(exp)s(onen)m(tial)29 b(in)f Fs(d)p Fu(.)42 b(Ho)m(w)m(ev)m(er,)31
b(w)m(e)e(exhibit)g(con\014gurations)f(where)h Fs(p)f
Fu(is)g(a)f(core)i(p)s(oin)m(t)f(but)g(is)g(con)m(tained)0
3781 y(in)j(only)g Fs(d)375 3745 y Fo(2)433 3781 y Fu(+)18
b(1)31 b(colourful)f(simplices.)46 b(W)-8 b(e)31 b(conjecture)h(that)e
(an)m(y)i(core)f(p)s(oin)m(t)g Fs(p)g Fu(of)f(an)m(y)h
Fs(d)p Fu(-dimensional)0 3897 y(colourful)41 b(con\014guration)f(is)h
(con)m(tained)h(in)f(at)f(least)h Fs(d)2102 3861 y Fo(2)2169
3897 y Fu(+)27 b(1)40 b(colourful)h(simplices.)69 b(Along)41
b(the)g(w)m(a)m(y)-8 b(,)0 4013 y(w)m(e)32 b(notice)f(that)f(b)s(oth)g
(in)h(the)g(colourful)g(and)f(mono)s(c)m(hrome)h(cases)h(the)f
(simplicial)h(depth)g(of)e(p)s(oin)m(ts)h(in)0 4129 y(general)37
b(p)s(osition)g(\(relativ)m(e)h(to)e(the)h(sample)h(set\))f(sometimes)h
(has)f(pleasan)m(t)h(parit)m(y)f(prop)s(erties.)57 b(W)-8
b(e)0 4246 y(conclude)42 b(b)m(y)f(men)m(tioning)h(some)f(other)g
(natural)f(problems)i(relating)e(to)g(the)h(colourful)g(and)f(mono-)0
4362 y(c)m(hrome)34 b(simplicial)g(depth.)1159 4580 y(2.)49
b Ft(Definitions)38 b(and)g(Ba)n(ck)n(gr)n(ound)0 4755
y Fu(2.1.)49 b FA(Simplicial)f(Depth.)i Fu(The)41 b(\(closed\))i
(simplicial)f(depth)g(of)e(a)h(p)s(oin)m(t)g Fs(p)g Fu(relativ)m(e)i
(to)d(a)h(set)h Fs(S)k Fu(of)0 4871 y Fs(n)30 b Fu(=)g
Fn(j)p Fs(S)6 b Fn(j)33 b Fu(p)s(oin)m(ts)h(in)g Fr(R)830
4835 y Fq(d)905 4871 y Fu(is)g(the)g(n)m(um)m(b)s(er)i(of)d(\(closed\))
i(simplices)h(generated)f(b)m(y)g(sets)g(of)e(\()p Fs(d)23
b Fu(+)g(1\))33 b(p)s(oin)m(ts)p 0 4970 499 4 v 100 5064
a Fz(2000)27 b Fm(Mathematics)32 b(Subje)l(ct)d(Classi\014c)l(ation.)44
b Fz(52C45,)25 b(52A35.)100 5161 y(Researc)n(h)34 b(supp)r(orted)i(b)n
(y)g(NSER)n(C)g(Disco)n(v)n(ery)e(gran)n(ts)g(for)i(the)g(four)g
(authors,)h(b)n(y)f(the)g(Canada)f(Researc)n(h)g(Chair)0
5261 y(program)26 b(for)h(the)h(\014rst)f(and)g(last)h(authors)e(and)i
(b)n(y)f(a)g(MIT)-7 b(A)n(CS)28 b(gran)n(t)e(for)h(the)h(second)f(and)h
(third)f(authors.)1931 5360 y Fl(1)p eop end
%%Page: 2 2
TeXDict begin 2 1 bop 0 75 a Fl(2)536 b(ANTOINE)25 b(DEZA,)g(SUI)f
(HUANG,)h(T)-6 b(AMON)25 b(STEPHEN)h(AND)e(T)-6 b(AM)2823
56 y(\023)2813 75 y(AS)25 b(TERLAKY)0 274 y Fu(from)34
b Fs(S)41 b Fu(con)m(taining)35 b Fs(p)f Fu(in)h(their)g(con)m(v)m(ex)i
(h)m(ull.)50 b(This)36 b(w)m(as)f(in)m(tro)s(duced)h(b)m(y)f(Liu)g
([Liu90])g(as)f(a)h(measure)0 390 y(of)e(ho)m(w)h(represen)m(tativ)m(e)
j Fs(p)c Fu(is)h(of)f(the)h(p)s(oin)m(ts)h(in)e Fs(S)6
b Fu(.)47 b(Denote)33 b(the)h(simplicial)h(depth)g(of)e
Fs(p)g Fu(relativ)m(e)i(to)e Fs(S)0 506 y Fu(as)e(depth)361
530 y Fq(S)412 506 y Fu(\()p Fs(p)p Fu(\).)43 b(The)31
b(simplicial)h(depth)f(of)f Fs(p)g Fu(can)h(b)s(e)f(in)m(terpreted)i
(as)f(the)g(probabilit)m(y)g(that)f Fs(p)g Fu(lies)i(in)e(a)0
623 y(random)35 b(simplex)i(of)d Fs(S)41 b Fu(times)36
b(a)f(constan)m(t)h(factor)e(of)h Fs(n)2128 586 y Fq(d)p
Fo(+1)2293 623 y Fu(if)g(w)m(e)h(sample)g(p)s(oin)m(ts)g(from)e
Fs(S)41 b Fu(uniformly)0 739 y(with)33 b(replacemen)m(t,)i(or)d(times)
1174 658 y Fk(\000)1261 695 y Fq(n)1220 773 y(d)p Fo(+1)1346
658 y Fk(\001)1424 739 y Fu(if)h(w)m(e)g(sample)h(without)f(replacemen)
m(t.)100 863 y(W)-8 b(e)29 b(are)f(most)h(in)m(terested)h(in)f(the)g
(case)g(when)h Fs(S)20 b Fn([)14 b(f)p Fs(p)p Fn(g)28
b Fu(is)h(in)g Fp(gener)-5 b(al)30 b(p)-5 b(osition)p
Fu(,)28 b(that)h(is)g(for)f(all)g Fs(k)j(<)c(d)0 979
y Fu(there)39 b(are)f(no)g Fs(k)s Fu(-dimensional)i(a\016ne)e
(subspaces)j(con)m(tain)e Fs(k)29 b Fu(+)d(2)38 b(p)s(oin)m(ts)h(from)f
Fs(S)31 b Fn([)c(f)p Fs(p)p Fn(g)p Fu(.)60 b(With)38
b(this)0 1096 y(assumption,)f Fs(p)d Fu(will)i(alw)m(a)m(ys)g(b)s(e)f
(in)g(the)g(in)m(terior)g(of)f(an)m(y)i(simplices)h(that)d(con)m(tain)h
(it,)h(so)e(the)i(notions)0 1212 y(of)c(closed)h(and)g(op)s(en)f
(simplicial)i(depth)f(coincide.)45 b(Without)33 b(this)g(assumption)g
(the)g(closed)g(simplicial)0 1328 y(depth)g(will)h(b)s(e)e(larger.)100
1444 y(F)-8 b(or)27 b(a)h(set)g(of)g(p)s(oin)m(ts)g Fs(S)6
b Fu(,)29 b(de\014ne)h Fs(f)11 b Fu(\()p Fs(S)6 b Fu(\))27
b(to)h(b)s(e)g(the)g(maxim)m(um)i(simplicial)f(depth)g(of)f(a)g(p)s
(oin)m(t)g Fs(p)g Fu(relativ)m(e)0 1560 y(to)k Fs(S)6
b Fu(,)33 b(that)f(is:)1475 1703 y Fs(f)11 b Fu(\()p
Fs(S)6 b Fu(\))27 b(=)h(max)1812 1773 y Fq(p)p Fj(2)p
Fq(R)1948 1754 y Fi(d)2005 1703 y Fu(depth)2249 1727
y Fq(S)2300 1703 y Fu(\()p Fs(p)p Fu(\))1350 b(\(1\))0
1926 y(A)25 b(p)s(oin)m(t)g Fs(p)g Fu(maximizing)h Fs(f)11
b Fu(\()p Fs(S)6 b Fu(\))25 b(can)g(b)s(e)g(understo)s(o)s(d)g(as)g(a)g
(higher)h(dimensional)g(median)g(p)s(oin)m(t.)41 b(W)-8
b(e)25 b(will)0 2042 y(call)k(an)m(y)g(suc)m(h)i Fs(p)d
Fu(a)h Fp(simplicial)h(me)-5 b(dian)p Fu(.)41 b(Indeed)30
b(for)e Fs(d)f Fu(=)h(1,)h(this)h(is)f(the)g(usual)h(de\014nition)f(of)
g(a)f(median)0 2159 y Fr(R)p Fu(.)69 b(In)41 b(higher)h(dimensions,)j
(this)d(de\014nition)g(retains)g(man)m(y)g(desirable)g(prop)s(erties)g
(of)f(the)g(median,)0 2275 y(suc)m(h)h(as)f(a\016ne)h(in)m(v)-5
b(ariance)42 b(and)f(a)f(high)i(breakdo)m(wn)g(p)s(oin)m(t)f(\(see)h
(e.g.)f([Alo04],)i([FR05)o(],)g([GSW92],)0 2391 y([Liu90]\).)g(Ho)m(w)m
(ev)m(er,)35 b(this)f(maxim)m(um)g(will)f(not)f(b)s(e)h(attained)g(at)f
(a)h(p)s(oin)m(t)f(in)h(general)g(p)s(osition.)100 2507
y(W)-8 b(e)48 b(will)g(consider)h(a)f(similar)g(quan)m(tit)m(y)-8
b(,)53 b(the)c(maxim)m(um)g(simplicial)g(depth)g(of)e(a)h(p)s(oin)m(t)f
Fs(p)h Fu(that)0 2623 y(main)m(tains)34 b Fs(S)28 b Fn([)22
b(f)p Fs(p)p Fn(g)32 b Fu(in)h(general)g(p)s(osition:)1173
2807 y Fs(g)t Fu(\()p Fs(S)6 b Fu(\))27 b(=)334 b(max)1496
2873 y Fq(S)t Fj([f)p Fq(p)p Fj(g)24 b Fo(in)f(general)h(p)r(osition)
2307 2807 y Fu(depth)2551 2830 y Fq(S)2602 2807 y Fu(\()p
Fs(p)p Fu(\))1048 b(\(2\))0 3058 y(Equiv)-5 b(alen)m(tly)d(,)27
b Fs(g)g Fu(is)c(the)h(maxim)m(um)h(op)s(en)e(simplicial)i(depth)e(of)g
(a)g(p)s(oin)m(t)g Fr(R)2751 3021 y Fq(d)2792 3058 y
Fu(.)40 b(In)23 b(this)h(w)m(a)m(y)g(the)g(de\014nition)0
3174 y(of)33 b Fs(g)j Fu(can)e(b)s(e)f(extended)i(to)e(the)h(case)g
(when)g Fs(S)39 b Fu(is)34 b(not)f(in)h(general)f(p)s(osition.)46
b(While)34 b(the)g(maxim)m(um)h(in)0 3290 y(\(1\))g(will)i(b)s(e)f
(attained)g(on)g(a)g(discrete)h(set)g(of)e(p)s(oin)m(ts)h(in)h
Fr(R)2213 3254 y Fq(d)2253 3290 y Fu(,)g(the)f(maxim)m(um)i(in)e(\(2\))
f(will)i(b)s(e)f(attained)0 3406 y(on)c(an)h(op)s(en)g(set.)44
b(F)-8 b(or)32 b(non-empt)m(y)h Fs(S)6 b Fu(,)33 b(w)m(e)g(will)h(ha)m
(v)m(e)g Fs(g)t Fu(\()p Fs(S)6 b Fu(\))26 b Fs(<)i(f)11
b Fu(\()p Fs(S)6 b Fu(\).)0 3634 y(2.2.)49 b FA(Colourful)29
b(Simplicial)i(Depth.)49 b Fu(No)m(w)26 b(consider)h(a)e(situation)h
(where)h(p)s(oin)m(ts)f(are)f(giv)m(en)h(in)g(eac)m(h)0
3750 y(of)35 b Fs(r)g Fn(\025)e Fs(d)24 b Fu(+)g(1)36
b(colours.)52 b(Then)37 b(the)f(sample)h(consists)g(of)e(colourful)h
(sets)g Fs(S)2834 3765 y Fo(1)2874 3750 y Fs(;)17 b(S)2978
3765 y Fo(2)3017 3750 y Fs(;)g(:)g(:)g(:)f(;)h(S)3296
3765 y Fq(r)3369 3750 y Fu(whic)m(h)37 b(de\014ne)0 3866
y(a)42 b(colourful)g(con\014guration)g FA(S)p Fu(.)72
b(In)42 b(the)h(follo)m(wing)f(w)m(e)h(use)g(a)f(b)s(old)f(fon)m(t)h
(for)g(colourful)g(ob)5 b(jects.)73 b(A)0 3982 y Fp(c)-5
b(olourful)32 b(simplex)d Fu(from)g(these)i(sets)g(is)g(an)m(y)f
(simplex)i(whose)f(v)m(ertices)h(are)e(c)m(hosen)h(from)f(distinct)h
(sets.)0 4099 y(W)-8 b(e)28 b(de\014ne)h FA(depth)722
4122 y Fh(S)771 4099 y Fu(\()p Fs(p)p Fu(\))f(the)g Fp(c)-5
b(olourful)30 b(simplicial)f(depth)f Fu(of)f Fs(p)h Fu(relativ)m(e)h
(to)e(the)i(con\014guration)e FA(S)i Fu(as)f(the)0 4215
y(n)m(um)m(b)s(er)j(of)f(colourful)g(simplices)j(con)m(taining)d
Fs(p)p Fu(.)43 b(As)30 b(with)h(mono)s(c)m(hrome)g(simplicial)g(depth,)
h(colourful)0 4331 y(depth)44 b(can)f(b)s(e)g(in)m(terpreted)h
(probabilistically)-8 b(.)76 b(In)43 b(the)h(case)f(where)h
Fs(r)k Fu(=)d Fs(d)29 b Fu(+)g(1,)45 b(colourful)e(depth)0
4447 y(corresp)s(onds)31 b(to)f(sp)s(ecifying)h(separate)f
(distributions)i(for)d(eac)m(h)i(v)m(ertex)g(of)f(the)g(simplex.)44
b(Dividing)31 b(the)0 4563 y(depth)f(b)m(y)h Fn(j)p Fs(S)494
4578 y Fo(1)533 4563 y Fn(j)16 b(\001)g(j)p Fs(S)709
4578 y Fo(2)747 4563 y Fn(j)g(\001)g Fs(:)h(:)g(:)e Fn(\001)h(j)p
Fs(S)1097 4578 y Fq(d)p Fo(+1)1227 4563 y Fn(j)29 b Fu(giv)m(es)i(the)f
(probabilit)m(y)g(that)g Fs(p)f Fu(lies)i(in)e(a)h(random)f(colourful)h
(simplex)0 4680 y(\(sampled)k(uniformly\).)100 4796 y(A)44
b(c)m(hoice)j(of)d(sets)i Fs(S)906 4811 y Fo(1)945 4796
y Fs(;)17 b(:)g(:)g(:)f(;)h(S)1224 4811 y Fq(r)1307 4796
y Fu(sp)s(eci\014es)47 b(a)d Fp(c)-5 b(olourful)46 b(c)-5
b(on\014gur)g(ation)44 b FA(S)h Fu(of)f(p)s(oin)m(ts.)81
b(W)-8 b(e)45 b(call)h(the)0 4912 y(in)m(tersection)38
b(of)d(the)h(con)m(v)m(ex)i(h)m(ulls)f(of)e(the)h Fs(S)1714
4927 y Fq(i)1742 4912 y Fu('s)h(in)e(a)h(con\014guration)g(the)g
Fp(c)-5 b(or)g(e)35 b Fu(of)g FA(S)p Fu(.)53 b(B\023)-49
b(ar\023)g(an)m(y)36 b(pro)m(v)m(ed)0 5028 y(that)43
b(core)h(p)s(oin)m(ts)g(are)g(con)m(tained)g(in)g(some)g(colourful)g
(simplex;)51 b(this)44 b(is)g(kno)m(wn)h(at)e(the)h(Colourful)0
5145 y(Carath)m(\023)-46 b(eo)s(dory)44 b(Theorem)h([B\023)-49
b(ar82].)77 b(In)45 b(the)f(remainder)h(of)f(the)g(pap)s(er,)j(except)e
(where)h(noted,)h(w)m(e)0 5261 y(assume)39 b(that)f(all)f
(con\014gurations)i(and)e Fs(p)h Fu(are)g(in)g(general)g(p)s(osition)g
(and)f(ha)m(v)m(e)i(a)f(non-empt)m(y)h(\(hence)p eop
end
%%Page: 3 3
TeXDict begin 3 2 bop 1304 71 a Fl(COLOURFUL)32 b(SIMPLICIAL)g(DEPTH)
1266 b(3)0 274 y Fu(full-dimensional\))35 b(core.)47
b(W)-8 b(e)34 b(remark)g(that)g(our)f(results)i(hold)f(under)h(w)m(eak)
m(er)g(conditions,)g(suc)m(h)g(as)f Fs(p)0 390 y Fu(not)e(lying)i(on)e
(an)m(y)h(h)m(yp)s(erplanes)i(generated)f(b)m(y)f(p)s(oin)m(ts)g(from)g
(the)g(con\014guration.)0 610 y(2.3.)49 b FA(Bac)m(kground.)g
Fu(Ev)m(en)h(b)s(efore)f(the)f(notion)h(of)f(simplicial)h(depth)h(w)m
(as)f(studied)h(in)e(statistics,)0 726 y(the)f(question)g(of)f
(computing)h(b)s(ounds)g(for)f Fs(f)11 b Fu(\()p Fs(S)6
b Fu(\))45 b(and)h Fs(g)t Fu(\()p Fs(S)6 b Fu(\))45 b(giv)m(en)j
Fs(n)e Fu(and)h Fs(d)e Fu(w)m(as)i(studied)h(in)f(the)0
843 y(com)m(binatorics)i(and)f(computational)g(geometry)h(comm)m
(unities.)91 b(The)49 b(t)m(w)m(o-dimensional)g(question)0
959 y(dates)31 b(bac)m(k)g(at)e(least)i(to)e(K\023)-49
b(arteszi)31 b([K\023)-49 b(ar55)o(])30 b(who)h(sho)m(w)m(ed)g(that)f
(for)g Fs(n)g Fu(p)s(oin)m(ts)g(in)g(the)h(plane,)g Fs(g)t
Fu(\()p Fs(S)6 b Fu(\))29 b(is)h(at)0 1075 y(most)262
1036 y Fo(1)p 245 1052 71 4 v 245 1109 a(24)325 1075
y Fu(\()p Fs(n)421 1039 y Fo(3)474 1075 y Fn(\000)13
b Fs(n)p Fu(\))29 b(for)f(o)s(dd)g Fs(n)g Fu(and)h(at)e(most)1671
1036 y Fo(1)p 1653 1052 V 1653 1109 a(24)1734 1075 y
Fu(\()p Fs(n)1830 1039 y Fo(3)1882 1075 y Fn(\000)13
b Fu(4)p Fs(n)p Fu(\))29 b(for)f(ev)m(en)i Fs(n)p Fu(,)f(and)g(sho)m(w)
m(ed)h(that)e(these)h(b)s(ounds)0 1191 y(w)m(ere)40 b(attained)g(when)g
Fs(S)45 b Fu(is)39 b(the)h(set)f(of)g(v)m(ertices)i(of)e(a)g(regular)g
Fs(n)p Fu(-gon.)62 b(In)39 b(the)h(early)g(1980's,)g(Boros)0
1314 y(and)28 b(F)s(\177)-51 b(uredi)27 b([BF84])h(sho)m(w)m(ed)i
Fs(g)t Fu(\()p Fs(S)6 b Fu(\))26 b(is)j(at)f(least)1799
1274 y Fq(n)1842 1251 y Fg(3)p 1799 1291 78 4 v 1802
1348 a Fo(27)1899 1314 y Fu(+)13 b Fs(O)s Fu(\()p Fs(n)2162
1278 y Fo(2)2200 1314 y Fu(\),)29 b(and)f(ga)m(v)m(e)h
(con\014gurations)g(ac)m(hieving)g(this)0 1430 y(b)s(ound.)100
1546 y(In)39 b(a)f(b)s(eautiful)h(pap)s(er,)i(B\023)-49
b(ar\023)g(an)m(y)39 b([B\023)-49 b(ar82])38 b(ga)m(v)m(e)i(b)s(ounds)g
(for)e(the)h(mono)s(c)m(hrome)h(simplicial)g(depth)0
1662 y(in)h(dimension)h Fs(d)f Fu(as)f(an)h(application)g(of)f(his)i
(Colourful)f(Carath)m(\023)-46 b(eo)s(dory)41 b(Theorem.)69
b(He)41 b(obtained)g(a)0 1779 y(lo)m(w)m(er)34 b(b)s(ound)f(b)m(y)h
(sho)m(wing)g(that)f(after)g(colouring)g(the)h(p)s(oin)m(ts,)f(some)h
(p)s(oin)m(t)f Fs(p)g Fu(m)m(ust)h(b)s(e)g(con)m(tained)g(in)0
1895 y(man)m(y)e(colourful)f(simplices.)46 b(A)31 b(k)m(ey)h(p)s(oin)m
(t)g(of)e(B\023)-49 b(ar\023)g(an)m(y's)32 b(pro)s(of)f(is)g(that)g(a)g
(core)g(p)s(oin)m(t)g Fs(p)g Fu(of)g(a)g(colourful)0
2011 y(con\014guration)41 b(m)m(ust)h(lie)g(in)f(at)g(least)g
Fp(one)g Fu(colourful)g(simplex.)71 b(Using)42 b(this)f(fact,)i(for)e
(a)g(set)g Fs(S)47 b Fu(of)41 b Fs(n)0 2127 y Fu(p)s(oin)m(ts)33
b(in)g(general)g(p)s(osition)g(in)g Fr(R)1301 2091 y
Fq(d)1374 2127 y Fu(B\023)-49 b(ar\023)g(an)m(y)33 b(obtains)g(a)f(lo)m
(w)m(er)i(b)s(ound)e(of:)1195 2363 y Fs(g)t Fu(\()p Fs(S)6
b Fu(\))27 b Fn(\025)1719 2296 y Fu(1)p 1530 2340 427
4 v 1530 2431 a(\()p Fs(d)22 b Fu(+)g(1\))1826 2403 y
Fq(d)p Fo(+1)1966 2223 y Fk(\022)2120 2296 y Fs(n)2040
2431 y(d)f Fu(+)h(1)2259 2223 y Fk(\023)2355 2363 y Fu(+)g
Fs(O)s Fu(\()p Fs(n)2627 2322 y Fq(d)2667 2363 y Fu(\))1070
b(\(3\))0 2604 y(This)42 b(result)f(is)h(asymptotically)g(sharp)f(up)g
(to)f(a)h(constan)m(t)g(factor)f(as)h(function)g(of)g
Fs(n)f Fu(\(for)g(\014xed)i Fs(d)p Fu(\).)0 2720 y(Ho)m(w)m(ev)m(er,)37
b(as)d(B\023)-49 b(ar\023)g(an)m(y)35 b(remarks,)g(the)g(constan)m(t)g
(is)f(probably)h(quite)g(far)e(from)h(the)h(truth.)48
b(Indeed,)35 b(he)0 2837 y(giv)m(es)f(a)e(sharp)h(upp)s(er)g(b)s(ound)g
(of:)1291 3059 y Fs(g)t Fu(\()p Fs(S)6 b Fu(\))27 b Fn(\024)1808
2992 y Fu(1)p 1626 3037 412 4 v 1626 3128 a(2)1675 3099
y Fq(d)1715 3128 y Fu(\()p Fs(d)22 b Fu(+)g(1\)!)2048
3059 y Fs(n)2106 3018 y Fq(d)p Fo(+1)2259 3059 y Fu(+)g
Fs(O)s Fu(\()p Fs(n)2531 3018 y Fq(d)2571 3059 y Fu(\))1166
b(\(4\))0 3294 y(W)-8 b(e)33 b(sp)s(eculate)h(that)e(the)h(true)g(lo)m
(w)m(er)h(b)s(ound)f(is)g(not)f(m)m(uc)m(h)i(less)g(than)f(the)g(upp)s
(er)g(b)s(ound.)100 3410 y(One)h(w)m(a)m(y)i(to)e(impro)m(v)m(e)i
(\(3\))e(w)m(ould)h(b)s(e)f(to)g(sho)m(w)i(that)e(a)g(core)g(p)s(oin)m
(t)h Fs(p)f Fu(m)m(ust)h(lie)g(in)g(more)f(than)h(one)0
3526 y(colorful)26 b(simplex.)43 b(In)26 b(B\023)-49
b(ar\023)g(an)m(y's)27 b(original)f(pap)s(er,)h(he)f(notes)h(that)e
Fs(p)h Fu(m)m(ust)h(in)f(fact)g(lie)g(in)g(at)g(least)g(\()p
Fs(d)8 b Fu(+)g(1\))0 3642 y(colourful)33 b(simplices,)i(thereb)m(y)f
(impro)m(ving)g(\(3\))e(to:)1241 3884 y Fs(g)t Fu(\()p
Fs(S)6 b Fu(\))26 b Fn(\025)1719 3816 y Fu(1)p 1575 3861
336 4 v 1575 3952 a(\()p Fs(d)c Fu(+)g(1\))1871 3923
y Fq(d)1921 3743 y Fk(\022)2075 3816 y Fs(n)1995 3952
y(d)f Fu(+)h(1)2214 3743 y Fk(\023)2310 3884 y Fu(+)g
Fs(O)s Fu(\()p Fs(n)2582 3842 y Fq(d)2622 3884 y Fu(\))1115
b(\(5\))0 4119 y(More)38 b(generally)-8 b(,)39 b(if)e(w)m(e)i(could)f
(sho)m(w)g(that)f(an)m(y)h(core)g(p)s(oin)m(t)g Fs(p)f
Fu(of)g(a)g Fs(d)p Fu(-dimensional)h(con\014guration)f(is)0
4235 y(con)m(tained)d(in)g(at)e(least)i Fs(\026)p Fu(\()p
Fs(d)p Fu(\))e(simplices,)k(then)e(w)m(e)g(can)f(impro)m(v)m(e)i(the)e
(constan)m(t)h(in)g(equation)g(\(3\))e(b)m(y)i(a)0 4352
y(factor)e(of)g Fs(\026)p Fu(\()p Fs(d)p Fu(\).)1055
4615 y(3.)49 b Ft(Colourfull)-7 b(y)40 b(Co)n(vering)e(the)f(Core)100
4789 y Fu(This)e(leads)g(us)f(to)g(ask:)47 b(What)34
b(is)g(the)h(minim)m(um)g(n)m(um)m(b)s(er)h Fs(\026)p
Fu(\()p Fs(d)p Fu(\))d(of)g(simplices)k(that)c(can)i(con)m(tain)f(a)0
4905 y(core)j(p)s(oin)m(t)g Fs(p)g Fu(in)g(a)g(colourful)g
(con\014guration?)57 b(Giv)m(en)37 b(a)g(colourful)g(con\014guration)g
FA(S)g Fu(with)h(colourful)0 5021 y(sets)c Fs(S)251 5036
y Fo(1)290 5021 y Fs(;)17 b(:)g(:)g(:)f(;)h(S)569 5036
y Fq(r)639 5021 y Fu(w)m(e)34 b(can)f(de\014ne:)1384
5201 y(m)q(\()p FA(S)p Fu(\))28 b(=)100 b(min)1735 5267
y Fq(p)p Fj(2)p Fo(core\()p Fh(S)p Fo(\))2060 5201 y
FA(depth)2341 5225 y Fh(S)2391 5201 y Fu(\()p Fs(p)p
Fu(\))1259 b(\(6\))p eop end
%%Page: 4 4
TeXDict begin 4 3 bop 0 75 a Fl(4)536 b(ANTOINE)25 b(DEZA,)g(SUI)f
(HUANG,)h(T)-6 b(AMON)25 b(STEPHEN)h(AND)e(T)-6 b(AM)2823
56 y(\023)2813 75 y(AS)25 b(TERLAKY)0 274 y Fu(W)-8 b(e)30
b(remark)h(that)f(if)g(core\()p FA(S)p Fu(\))g(has)h(a)e(non-empt)m(y)j
(in)m(terior,)f(the)f(minim)m(um)i(in)e(\(6\))g(will)h(b)s(e)f
(attained)g(on)0 390 y(an)i(op)s(en)h(set)h(of)e(p)s(oin)m(ts)h(that)f
(are)h(in)g(general)g(p)s(osition)f(relativ)m(e)i(to)e
FA(S)p Fu(.)100 506 y(In)26 b(this)i(notation,)f(our)f(ob)5
b(jectiv)m(e)29 b(is)e(to)f(\014nd)h(the)g(minim)m(um)h(v)-5
b(alue)27 b(of)f(m)q(\()p FA(S)p Fu(\))g(o)m(v)m(er)i(all)e
(con\014gurations)0 623 y FA(S)i Fu(with)h(full-dimensional)g(core)f
(in)g(dimension)h Fs(d)p Fu(.)42 b(F)-8 b(or)27 b(a)g(\014xed)i
Fs(d)p Fu(,)g(it)f(is)g(clear)g(that)g(some)h(con\014guration)0
739 y(with)k(\()p Fs(d)22 b Fu(+)g(1\))32 b(p)s(oin)m(ts)i(in)e(eac)m
(h)i(of)e(\()p Fs(d)22 b Fu(+)g(1\))32 b(colours)h(attains)g(this)g
(minim)m(um,)i(whic)m(h)f(dep)s(ends)g(only)f(on)0 855
y(the)g(dimension.)45 b(Hence)34 b(w)m(e)g(can)e(de\014ne:)1095
1012 y Fs(\026)p Fu(\()p Fs(d)p Fu(\))27 b(=)407 b(min)1412
1078 y Fq(d)24 b Fo(con\014gurations)h Fh(S)p Fq(;)32
b(p)p Fj(2)p Fo(core\()p Fh(S)p Fo(\))2349 1012 y FA(depth)2630
1035 y Fh(S)2680 1012 y Fu(\()p Fs(p)p Fu(\))970 b(\(7\))100
1229 y(One)32 b(migh)m(t)h(supp)s(ose)g(that)f(m)q(\()p
FA(S)p Fu(\))g(is)h(often)f(large.)43 b(As)33 b(a)f(though)m(t)g(exp)s
(erimen)m(t,)j(consider)e(c)m(ho)s(osing)0 1345 y(a)d(con\014guration)h
(at)f(random.)43 b(If)31 b(w)m(e)h(tak)m(e)f(\()p Fs(d)18
b Fu(+)g(1\))30 b(p)s(oin)m(ts)i(in)e Fr(R)2420 1309
y Fq(d)2491 1345 y Fu(from)h(a)f(distribution)i(that)e(is)h(\\nice")0
1461 y(and)45 b(cen)m(trally)h(symmetric)h(ab)s(out)e(the)g(origin)g
FA(0)p Fu(,)j(the)d(probabilit)m(y)h(that)e FA(0)h Fu(is)g(con)m
(tained)h(in)f(their)0 1577 y(con)m(v)m(ex)c(h)m(ull)f(is)658
1538 y Fo(1)p 640 1554 72 4 v 640 1612 a(2)675 1593 y
Fi(d)760 1577 y Fu(\(see)g(e.g.)f([WW01]\).)63 b(This)40
b(suggests)h(that)e(for)f(random)h FA(S)p Fu(,)i(a)e(t)m(ypical)h(v)-5
b(alue)39 b(for)0 1702 y FA(depth)282 1726 y Fh(S)331
1702 y Fu(\()p FA(0)p Fu(\))32 b(w)m(ould)i(b)s(e)940
1663 y Fo(1)p 922 1680 V 922 1737 a(2)957 1718 y Fi(d)1004
1702 y Fu(\()p Fs(d)21 b Fu(+)h(1\))1299 1666 y Fq(d)p
Fo(+1)1430 1702 y Fu(.)43 b(F)-8 b(or)32 b(a)g(set)h
Fs(S)39 b Fu(of)32 b(\()p Fs(d)21 b Fu(+)h(1\))2413 1666
y Fo(2)2485 1702 y Fu(p)s(oin)m(ts)33 b(in)g(the)g(plane,)g(plugging)f
(this)0 1820 y(v)-5 b(alue)28 b(in)m(to)h(B\023)-49 b(ar\023)g(an)m
(y's)29 b(analysis)g(giv)m(es)h(us)e(an)g(estimate)h(of)f
Fs(g)t Fu(\()p Fs(S)6 b Fu(\))27 b(v)m(ery)i(close)g(to)f(B\023)-49
b(ar\023)g(an)m(y's)29 b(upp)s(er)g(b)s(ound)0 1936 y(\(4\).)43
b(Ho)m(w)m(ev)m(er,)34 b(it)d(is)h(not)f(immediately)i(clear)f(if)f(w)m
(e)h(should)g(exp)s(ect)h(m\()p FA(S)p Fu(\))e(to)g(b)s(e)h(m)m(uc)m(h)
h(smaller)f(than)0 2053 y FA(depth)282 2076 y Fh(S)331
2053 y Fu(\()p FA(0)p Fu(\).)100 2179 y(If)40 b(w)m(e)i(tak)m(e)g(a)f
(con\014guration)g FA(S)1328 2143 y Fj(4)1436 2179 y
Fu(with)g Fs(S)1732 2132 y Fj(4)1726 2204 y Fo(1)1840
2179 y Fu(giv)m(en)h(b)m(y)g(\()p Fs(d)27 b Fu(+)h(1\))41
b(p)s(oin)m(ts)g(in)g(general)h(p)s(osition)f(and)0 2306
y Fs(S)66 2258 y Fj(4)60 2330 y Fo(1)164 2306 y Fu(=)31
b Fs(S)337 2258 y Fj(4)331 2330 y Fo(2)435 2306 y Fu(=)g
Fs(:)17 b(:)g(:)30 b Fu(=)h Fs(S)860 2258 y Fj(4)854
2333 y Fq(d)p Fo(+1)1020 2306 y Fu(w)m(e)k(get)g(m\()p
FA(S)1511 2269 y Fj(4)1578 2306 y Fu(\))c(=)g(\()p Fs(d)23
b Fu(+)h(1\)!.)49 b(In)35 b(Section)h(3.4)e(w)m(e)i(exhibit)f(a)g
(con\014guration)0 2428 y FA(S)62 2391 y Fj(\000)154
2428 y Fu(with)e(m\()p FA(S)557 2391 y Fj(\000)617 2428
y Fu(\))27 b Fn(\024)h Fs(d)838 2391 y Fo(2)900 2428
y Fu(+)22 b(1.)100 2544 y(In)27 b(the)h(remainder)h(of)e(the)g(pap)s
(er,)i(except)g(where)g(noted,)g(w)m(e)f(consider)h(con\014gurations)f
(with)g(\()p Fs(d)12 b Fu(+)g(1\))0 2660 y(p)s(oin)m(ts)33
b(in)g(eac)m(h)g(of)g(\()p Fs(d)21 b Fu(+)h(1\))33 b(colours.)0
2834 y(3.1.)49 b FA(Preliminaries.)h Fu(In)34 b([BO97b],)g(B\023)-49
b(ar\023)g(an)m(y)34 b(and)g(Onn)g(consider)h(the)g(problem)f(of)g
Fp(c)-5 b(olourful)36 b(line)-5 b(ar)0 2951 y(pr)g(o)g(gr)g(amming)p
Fu(.)41 b(This)31 b(is)g(the)g(algorithmic)f(v)m(ersion)i(of)e(the)g
(colourful)h(Carath)m(\023)-46 b(eo)s(dory)30 b(problem:)43
b(Giv)m(en)0 3067 y(a)c(core)h(p)s(oin)m(t)g Fs(p)p Fu(,)i(ho)m(w)e
(can)g(w)m(e)h Fp(\014nd)e Fu(a)g(colourful)h(simplex)i(con)m(taining)e
Fs(p)p Fu(?)65 b(They)41 b(b)s(egin)f(with)g(some)0 3183
y(prepro)s(cessing)34 b(whic)m(h)g(is)g(also)e(helpful)i(here.)100
3299 y(T)-8 b(ak)m(e)33 b(a)g(colourful)f(con\014guration)h
FA(S)g Fu(of)f(\()p Fs(d)21 b Fu(+)h(1\))32 b(colourful)h(sets)h(in)f
Fr(R)2725 3263 y Fq(d)2765 3299 y Fu(,)g FA(S)28 b Fu(=)f
Fn(f)p Fs(S)3128 3314 y Fo(1)3167 3299 y Fs(;)17 b(:)g(:)g(:)f(;)h(S)
3446 3314 y Fq(d)p Fo(+1)3577 3299 y Fn(g)p Fu(.)43 b(T)-8
b(ak)m(e)0 3416 y Fs(p)38 b Fn(2)g Fu(in)m(t)q(\(core\()p
FA(S)p Fu(\)\).)62 b(Without)39 b(loss)g(of)g(generalit)m(y)g(w)m(e)h
(assume)g(that)f(the)g(core)g(p)s(oin)m(t)g Fs(p)e Fu(=)h
FA(0)p Fu(.)62 b(Giv)m(en)0 3532 y(an)m(y)33 b(\014nite)h(set)f(of)f(p)
s(oin)m(ts)i Fs(T)41 b Fn(\022)28 b Fr(R)1266 3496 y
Fq(d)1307 3532 y Fu(,)33 b(scaling)g(the)g(p)s(oin)m(ts)g(of)f
Fs(T)47 b Fu(do)s(es)33 b(not)f(a\013ect)h(whether)h
FA(0)f Fu(lies)h(in)f(the)0 3648 y(con)m(v)m(ex)k(h)m(ull)g(of)d
Fs(T)49 b Fu(since)37 b(the)f(co)s(e\016cien)m(ts)h(in)f(a)f(con)m(v)m
(ex)i(com)m(bination)g(can)e(themselv)m(es)k(b)s(e)c(rescaled.)0
3764 y(This)f(allo)m(ws)f(us)g(to)g(normalize)g FA(S)g
Fu(b)m(y)g(rescaling)h(its)f(p)s(oin)m(ts)g(to)f(unit)h(v)m(ectors.)100
3880 y(Let)e(con)m(v)s(\()p Fs(T)14 b Fu(\))31 b(b)s(e)h(the)g(con)m(v)
m(ex)i(h)m(ull)e(of)f(the)h(p)s(oin)m(ts)g(in)g Fs(T)45
b Fu(and)32 b(cone)q(\()p Fs(T)14 b Fu(\))31 b(b)s(e)h(the)g(set)g(of)f
(non-negativ)m(e)0 3997 y(linear)k(com)m(binations)h(of)e(p)s(oin)m(ts)
h(of)g Fs(T)14 b Fu(.)49 b(A)34 b(cone)i(is)f Fp(simplicial)e
Fu(if)h(it)h(can)g(b)s(e)g(generated)g(b)m(y)h(a)e(set)h(of)f
Fs(d)0 4113 y Fu(linearly)29 b(indep)s(enden)m(t)i(p)s(oin)m(ts)e(in)f
Fr(R)1364 4077 y Fq(d)1405 4113 y Fu(.)42 b(If)28 b Fs(T)41
b Fn(\022)29 b Fr(R)1843 4077 y Fq(d)1911 4113 y Fu(is)g(a)f(set)h(of)f
(p)s(oin)m(ts,)i FA(0)39 b Fs(=)-60 b Fn(2)28 b Fs(T)14
b Fu(,)29 b(but)f FA(0)g Fn(2)g Fu(con)m(v)s(\()p Fs(T)14
b Fu(\),)28 b(then)0 4229 y(cone)q(\()p Fs(T)14 b Fu(\))38
b(m)m(ust)j(con)m(tain)e(a)g(non-trivial)h(linear)f(subspace)i(of)e
Fr(R)2430 4193 y Fq(d)2471 4229 y Fu(.)63 b(A)39 b(closed,)j(con)m(v)m
(ex)g(cone)d(is)h(called)0 4345 y Fp(p)-5 b(ointe)g(d)32
b Fu(if)g(it)h(do)s(es)g(not)f(con)m(tain)h(suc)m(h)h(a)f(subspace,)h
(so)f(w)m(e)h(summarize)g(this)f(as:)0 4513 y FA(Lemma)38
b(3.1.)j Fp(Given)33 b(any)h(\014nite)g(set)f(of)h(non-zer)-5
b(o)33 b(p)-5 b(oints)33 b Fs(T)41 b Fn(\022)29 b Fr(R)2555
4476 y Fq(d)2595 4513 y Fp(,)34 b FA(0)g Fp(is)f(in)h
Fu(con)m(v)r(\()p Fs(T)14 b Fu(\))34 b Fp(if)f(and)h(only)f(if)0
4629 y Fu(cone)q(\()p Fs(T)14 b Fu(\))34 b Fp(is)h(not)g(p)-5
b(ointe)g(d.)100 4796 y Fu(When)32 b Fs(T)45 b Fu(is)31
b(a)g(\014nite)h(set)g(of)f(p)s(oin)m(ts)g(on)h(the)f(unit)h
Fs(d)p Fu(-sphere)g Fr(S)2408 4760 y Fq(d)2476 4796 y
Fn(\022)c Fr(R)2653 4760 y Fq(d)2694 4796 y Fu(,)j(Lemma)h(3.1)f(is)g
(equiv)-5 b(alen)m(t)33 b(to)0 4912 y(sa)m(ying)d(that)f
FA(0)f Fn(2)g Fu(con)m(v)r(\()p Fs(T)14 b Fu(\))29 b(if)g(and)g(only)h
(if)f Fs(T)42 b Fu(is)30 b(not)f(con)m(tained)h(in)f(an)m(y)h(op)s(en)f
(hemisphere)j(of)c Fr(S)3616 4876 y Fq(d)3657 4912 y
Fu(.)43 b(One)0 5028 y(direction)f(is)g(pro)m(v)m(ed)h(b)m(y)g
(building)f(a)f(hemisphere)j(from)e(a)f(h)m(yp)s(erplane)i(through)f
FA(0)f Fu(whose)i(normal)0 5145 y(lies)c(in)e(the)h(in)m(terior)h(of)e
(cone\()p Fs(T)14 b Fu(\))38 b(when)g(this)g(cone)h(is)f(p)s(oin)m
(ted.)59 b(The)39 b(other)e(direction)i(is)f(pro)m(v)m(ed)h(b)m(y)0
5261 y(observing)34 b(that)e(an)h(op)s(en)f(hemisphere)j(nev)m(er)f
(con)m(tains)g(b)s(oth)e(a)h(p)s(oin)m(t)f Fs(p)h Fu(and)g(its)g(an)m
(tip)s(o)s(de)f Fn(\000)p Fs(p)p Fu(.)p eop end
%%Page: 5 5
TeXDict begin 5 4 bop 1304 71 a Fl(COLOURFUL)32 b(SIMPLICIAL)g(DEPTH)
1266 b(5)100 274 y Fu(W)-8 b(e)43 b(w)m(ould)h(lik)m(e)g(to)e(put)i
(Lemma)f(3.1)f(in)i(a)e(form)h(that)f(is)i(con)m(v)m(enien)m(t)h(for)e
(coun)m(ting)g(ho)m(w)h(man)m(y)0 390 y(simplices)h(generated)f(from)f
Fs(T)57 b Fu(con)m(tain)44 b FA(0)p Fu(.)75 b(T)-8 b(o)43
b(do)g(this,)j(w)m(e)f(\014nd)e(it)g(helpful)h(to)f(think)h(ab)s(out)f
(the)0 506 y(an)m(tip)s(o)s(de)33 b(of)f(one)h(of)f(the)h(p)s(oin)m
(ts.)0 706 y FA(Lemma)h(3.2.)k Fp(If)30 b Fs(T)41 b Fu(=)28
b Fn(f)p Fs(p)1003 721 y Fo(1)1042 706 y Fs(;)17 b(p)1135
721 y Fo(2)1174 706 y Fs(;)g(:)g(:)g(:)f(;)h(p)1442 721
y Fq(d)p Fo(+1)1572 706 y Fn(g)30 b Fp(is)h(a)f(set)h(of)f(non-zer)-5
b(o)29 b(a\016nely)h(indep)-5 b(endent)29 b(p)-5 b(oints)31
b(in)f Fr(R)3830 670 y Fq(d)3870 706 y Fp(,)0 822 y FA(0)35
b Fp(is)g(in)f Fu(con)m(v)s(\()p Fs(T)14 b Fu(\))34 b
Fp(if)h(and)f(only)h(if)f(the)h(antip)-5 b(o)g(de)34
b Fn(\000)p Fs(p)1957 837 y Fq(d)p Fo(+1)2123 822 y Fp(is)h(in)f
Fu(cone)q(\()p Fs(p)2624 837 y Fo(1)2663 822 y Fs(;)17
b(p)2756 837 y Fo(2)2795 822 y Fs(;)g(:)g(:)g(:)f(;)h(p)3063
837 y Fq(d)3103 822 y Fu(\))p Fp(.)0 1022 y(Pr)-5 b(o)g(of.)41
b Fu(Let)35 b Fs(K)j Fu(=)30 b(cone)q(\()p Fs(p)979 1037
y Fo(1)1018 1022 y Fs(;)17 b(p)1111 1037 y Fo(2)1150
1022 y Fs(;)g(:)g(:)g(:)f(;)h(p)1418 1037 y Fq(d)1458
1022 y Fu(\).)49 b(Since)35 b Fs(K)42 b Fu(is)35 b(a)f(cone)h
(generated)g(b)m(y)g Fs(d)f Fu(linearly)i(indep)s(enden)m(t)0
1138 y(p)s(oin)m(ts)j(in)f Fr(R)490 1102 y Fq(d)531 1138
y Fu(,)h Fs(K)46 b Fu(is)38 b(simplicial)i(and)e(hence)i(p)s(oin)m
(ted.)61 b(If)38 b Fn(\000)p Fs(p)2377 1153 y Fq(d)p
Fo(+1)2546 1138 y Fn(2)f Fs(K)7 b Fu(,)40 b(then)f(w)m(e)g(can)g(write)
g(it)f(as)g(a)0 1263 y(conic)f(com)m(bination)g(of)f(the)g(remaining)h
Fs(p)1606 1278 y Fq(i)1634 1263 y Fu(,)g(that)f(is:)52
b Fn(\000)p Fs(p)2183 1278 y Fq(d)p Fo(+1)2341 1263 y
Fu(=)2445 1188 y Fk(P)2550 1214 y Fq(d)2550 1292 y(i)p
Fo(=1)2685 1263 y Fs(a)2736 1278 y Fq(i)2764 1263 y Fs(p)2813
1278 y Fq(i)2878 1263 y Fu(for)35 b(some)i Fs(a)3329
1278 y Fo(1)3369 1263 y Fs(;)17 b(:)g(:)g(:)f(;)h(a)3639
1278 y Fq(d)3713 1263 y Fn(\025)34 b Fu(0.)0 1395 y(Mo)m(ving)27
b(the)f Fs(p)553 1410 y Fq(d)p Fo(+1)710 1395 y Fu(term)g(to)g(the)h
(righ)m(t)f(hand)g(side)h(of)f(the)g(equation)h(and)f(dividing)h(b)m(y)
g(1)9 b(+)3349 1320 y Fk(P)3453 1346 y Fq(d)3453 1424
y(i)p Fo(=1)3588 1395 y Fs(a)3639 1410 y Fq(i)3694 1395
y Fu(giv)m(es)0 1511 y FA(0)37 b Fu(as)g(a)g(con)m(v)m(ex)i(com)m
(bination)f(of)e(the)i Fs(p)1524 1526 y Fq(i)1552 1511
y Fu('s.)57 b(If)37 b Fn(\000)p Fs(p)1929 1526 y Fq(d)p
Fo(+1)2097 1511 y Fu(is)h(not)f(in)g Fs(K)7 b Fu(,)38
b(then)g(w)m(e)g(can)f(strictly)h(separate)0 1627 y Fn(\000)p
Fs(p)126 1642 y Fq(d)p Fo(+1)294 1627 y Fu(from)g Fs(K)44
b Fu(with)38 b(a)f(h)m(yp)s(erplane)i Fs(H)45 b Fu(through)38
b FA(0)p Fu(.)58 b(Then)38 b(b)s(oth)g Fs(K)44 b Fu(and)38
b Fs(p)2983 1642 y Fq(d)p Fo(+1)3151 1627 y Fu(lie)f(strictly)i(on)f
(the)0 1743 y(same)33 b(side)h(of)e Fs(H)8 b Fu(,)32
b(and)h(the)g(cone)g(generated)h(b)m(y)f Fs(T)46 b Fu(m)m(ust)34
b(b)s(e)f(p)s(oin)m(ted.)1140 b Ff(\003)0 2006 y Fu(3.2.)49
b FA(A)43 b(V)-9 b(ariational)44 b(Approac)m(h.)49 b
Fu(T)-8 b(ak)m(e)39 b(a)f(p)s(oin)m(t)g Fs(p)g Fu(from)f(a)h(\014nite)g
(set)h Fs(S)j Fn(2)37 b Fr(R)3152 1970 y Fq(d)3193 2006
y Fu(.)59 b(Call)38 b(a)g(simplex)0 2123 y(generated)d(b)m(y)h(p)s(oin)
m(ts)f(in)f Fs(S)40 b Fu(a)34 b Fs(p)p Fp(-simplex)f
Fu(if)i Fs(p)f Fu(is)h(one)g(of)f(the)g(p)s(oin)m(ts)h(used)h(to)e
(generate)h(the)g(simplex,)0 2239 y(and)j(call)h(a)f
Fs(p)p Fu(-simplex)h Fp(zer)-5 b(o-c)g(ontaining)37 b
Fu(if)h(it)g(con)m(tains)h FA(0)f Fu(in)h(its)g(in)m(terior.)60
b(De\014ne)39 b Fs(z)3287 2254 y Fq(S)3338 2239 y Fu(\()p
Fs(p)p Fu(\))f(to)g(b)s(e)h(the)0 2355 y(n)m(um)m(b)s(er)34
b(of)e(zero-con)m(taining)h Fs(p)p Fu(-simplices)i(for)d(a)g(giv)m(en)i
Fs(S)6 b Fu(.)100 2471 y(Lemma)31 b(3.2)g(tells)h(us)g(that)f
Fs(z)1186 2486 y Fq(S)1237 2471 y Fu(\()p Fs(p)p Fu(\))g(is)g(the)h(n)m
(um)m(b)s(er)g(of)f(simplicial)i(cones)f(generated)g(b)m(y)g
Fs(S)25 b Fn(n)19 b(f)p Fs(p)p Fn(g)30 b Fu(that)0 2588
y(con)m(tain)e Fn(\000)p Fs(p)p Fu(.)42 b(W)-8 b(e)27
b(\014nd)h(it)f(useful)i(to)d(think)j(ab)s(out)d(what)i(happ)s(ens)g
(to)f Fs(z)2667 2603 y Fq(S)2718 2588 y Fu(\()p Fs(p)p
Fu(\))g(if)g(w)m(e)h(mo)m(v)m(e)h Fs(p)e Fu(while)h(\014xing)0
2704 y(the)36 b(remaining)h(p)s(oin)m(ts)f(of)g Fs(S)6
b Fu(.)53 b(This)37 b(is)f(particularly)h(illustrativ)m(e)h(if)d(w)m(e)
i(con\014ne)g Fs(p)f Fu(to)f(the)i(surface)f(of)0 2820
y(the)d(unit)g(sphere)h Fr(S)733 2784 y Fq(d)806 2820
y Fu(cen)m(tred)g(at)f FA(0)p Fu(.)100 2936 y(Let)43
b Fs(U)56 b Fu(=)45 b Fs(S)35 b Fn(n)29 b(f)p Fs(p)p
Fn(g)42 b Fu(with)i Fn(j)p Fs(U)10 b Fn(j)45 b Fu(=)h
Fs(u)p Fu(.)74 b(Initially)44 b Fs(z)2006 2951 y Fq(S)2057
2936 y Fu(\()p Fs(p)p Fu(\))e(will)i(b)s(e)f(the)h(n)m(um)m(b)s(er)g
(of)e(simplicial)j(cones)0 3052 y(generated)29 b(b)m(y)g(sets)g(of)e
Fs(d)h Fu(p)s(oin)m(ts)h(from)e Fs(U)39 b Fu(that)28
b(con)m(tain)g Fn(\000)p Fs(p)p Fu(.)43 b(No)m(w)28 b(consider)i(what)e
(happ)s(ens)h(as)f Fs(p)g Fu(\(and)0 3169 y(hence)37
b Fn(\000)p Fs(p)p Fu(\))f(mo)m(v)m(e.)55 b(The)37 b(v)-5
b(alue)36 b(of)f Fs(z)1392 3184 y Fq(S)1443 3169 y Fu(\()p
Fs(p)p Fu(\))h(will)g(sta)m(y)h(\014xed)g(un)m(til)g
Fn(\000)p Fs(p)f Fu(crosses)h(the)g(b)s(oundary)f(of)f(some)0
3285 y(simplicial)41 b(cone)g(from)f Fs(U)10 b Fu(.)66
b(These)41 b(b)s(oundaries)g(are)f(de\014ned)h(b)m(y)g(the)f(h)m(yp)s
(erplanes)i(generated)f(b)m(y)g FA(0)0 3401 y Fu(and)34
b(sets)h(of)e(\()p Fs(d)22 b Fn(\000)i Fu(1\))33 b(p)s(oin)m(ts)i(from)
e Fs(U)10 b Fu(.)48 b(T)-8 b(aking)34 b(all)f(\()p Fs(d)23
b Fn(\000)g Fu(1\))34 b(sets)h(from)e Fs(U)10 b Fu(,)35
b(w)m(e)g(can)f(generate)g(all)f(suc)m(h)0 3517 y(b)s(oundaries.)44
b(They)34 b(divide)g(the)f(surface)g(of)f Fr(S)1738 3481
y Fq(d)1812 3517 y Fu(in)m(to)g(op)s(en)h Fp(c)-5 b(el)5
b(ls)32 b Fu(that)g(are)h(\()p Fs(d)21 b Fn(\000)i Fu(1\)-dimensional)
33 b(op)s(en)0 3634 y(sets.)52 b(W)-8 b(e)35 b(can)g(de\014ne)i(the)e
Fp(depth)g Fu(of)f(a)h(cell)g(of)g Fs(S)41 b Fu(to)34
b(b)s(e)h(the)h(n)m(um)m(b)s(er)g(of)f(simplicial)h(cones)g(generated)0
3750 y(b)m(y)d Fs(S)39 b Fu(con)m(taining)33 b(an)m(y)g(giv)m(en)h(p)s
(oin)m(t)f(in)f(the)h(in)m(terior)h(of)e(the)h(cell.)100
3866 y(Consider)40 b(mo)m(ving)g Fs(p)f Fu(along)g(the)g(surface)h(of)e
Fr(S)1897 3830 y Fq(d)1977 3866 y Fu(to)h(a)g(new)h(p)s(oin)m(t)f
Fs(p)2708 3830 y Fj(0)2731 3866 y Fu(.)63 b(If)39 b Fn(\000)p
Fs(p)g Fu(and)g Fn(\000)p Fs(p)3412 3830 y Fj(0)3475
3866 y Fu(are)g(in)h(the)0 3982 y(same)31 b(cell,)h(w)m(e)f(will)g(ha)m
(v)m(e)h Fs(z)1032 3997 y Fq(S)1083 3982 y Fu(\()p Fs(p)p
Fu(\))27 b(=)h Fs(z)1384 3997 y Fq(S)1435 3982 y Fu(\()p
Fs(p)1522 3946 y Fj(0)1545 3982 y Fu(\).)43 b(No)m(w)30
b(supp)s(ose)i Fn(\000)p Fs(p)f Fu(is)f(in)h(a)f(cell)h
Fs(C)37 b Fu(adjacen)m(t)31 b(to)f(the)h(cell)g Fs(C)3877
3946 y Fj(0)0 4099 y Fu(con)m(taining)f Fn(\000)p Fs(p)597
4062 y Fj(0)621 4099 y Fu(.)42 b(Then)31 b(as)e(w)m(e)i(mo)m(v)m(e)f
(from)f Fn(\000)p Fs(p)h Fu(to)f Fn(\000)p Fs(p)2072
4062 y Fj(0)2125 4099 y Fu(w)m(e)i(cross)f(a)f(single)h(h)m(yp)s
(erplane)h Fs(H)37 b Fu(de\014ned)31 b(b)m(y)0 4215 y(a)h(set)g
Fs(U)308 4179 y Fo(0)380 4215 y Fu(of)g(\()p Fs(d)20
b Fn(\000)h Fu(1\))32 b(p)s(oin)m(ts)g(from)g Fs(U)43
b Fu(b)s(elonging)32 b(to)f Fs(H)8 b Fu(.)43 b(Let's)33
b(sa)m(y)f(that)g Fn(\000)p Fs(p)g Fu(is)h(on)f(the)g(left)g(of)f
Fs(H)40 b Fu(and)0 4331 y Fn(\000)p Fs(p)126 4295 y Fj(0)183
4331 y Fu(is)33 b(on)g(the)g(righ)m(t.)45 b(F)-8 b(or)32
b(the)i(momen)m(t)g(w)m(e)g(will)f(assume)i(that)e(only)g(\()p
Fs(d)22 b Fn(\000)h Fu(1\))32 b(p)s(oin)m(ts)i(of)f Fs(U)43
b Fu(lie)34 b(on)e Fs(H)8 b Fu(.)0 4447 y(Let)31 b Fs(U)249
4411 y Fj(\000)339 4447 y Fu(b)s(e)g(the)g(set)g(of)g
Fs(k)i Fu(p)s(oin)m(ts)e(from)g Fs(U)41 b Fu(on)31 b(the)g(left)f(of)h
Fs(H)8 b Fu(,)30 b(and)h Fs(U)2595 4411 y Fo(+)2685 4447
y Fu(b)s(e)g(the)g Fs(u)18 b Fn(\000)h Fs(k)i Fn(\000)e
Fu(\()p Fs(d)e Fn(\000)i Fu(1\))30 b(p)s(oin)m(ts)0 4563
y(from)k Fs(U)44 b Fu(on)34 b(the)h(righ)m(t.)48 b(Since)35
b Fn(\000)p Fs(p)f Fu(is)h(in)f(a)g(cell)h(b)s(ordered)f(b)m(y)h
Fs(H)8 b Fu(,)34 b(it)g(lies)h(in)f(the)h(cone)f(de\014ned)i(b)m(y)f
(the)0 4680 y(p)s(oin)m(ts)d(from)e Fs(U)596 4644 y Fo(0)667
4680 y Fu(and)h Fs(x)h Fu(for)e(an)m(y)h(p)s(oin)m(t)h
Fs(x)c Fn(2)g Fs(U)1778 4644 y Fj(\000)1837 4680 y Fu(.)43
b(On)31 b(the)h(other)f(hand,)g Fn(\000)p Fs(p)h Fu(is)f(separated)h(b)
m(y)g Fs(H)38 b Fu(from)0 4796 y(the)30 b(cones)g(formed)g(b)m(y)g
Fs(U)955 4760 y Fo(0)1024 4796 y Fu(and)g Fs(y)i Fu(for)d(an)m(y)h
Fs(y)h Fn(2)d Fs(U)1867 4760 y Fo(+)1927 4796 y Fu(.)42
b(Hence)31 b Fn(\000)p Fs(p)e Fu(is)h(con)m(tained)h(in)e(exactly)i
Fs(k)h Fu(simplicial)0 4912 y(cones)c(from)f Fs(S)33
b Fu(generated)28 b(b)m(y)h Fs(U)1219 4876 y Fo(0)1286
4912 y Fu(and)e(a)g(single)h(other)g(p)s(oin)m(t.)42
b(Similarly)-8 b(,)29 b Fn(\000)p Fs(p)2908 4876 y Fj(0)2959
4912 y Fu(is)f(con)m(tained)g(in)g(exactly)0 5028 y Fs(u)23
b Fn(\000)h Fs(k)i Fn(\000)e Fu(\()p Fs(d)f Fn(\000)g
Fu(1\))34 b(suc)m(h)i(cones.)49 b(Simplicial)36 b(cones)f(that)f(do)g
(not)g(con)m(tain)h Fs(U)2877 4992 y Fo(0)2952 5028 y
Fu(in)f(their)h(generating)f(set)0 5145 y(will)f(not)f(ha)m(v)m(e)h
Fs(H)39 b Fu(as)32 b(a)g(facet,)h(so)f(they)h(will)f(con)m(tain)h
Fn(\000)p Fs(p)f Fu(if)g(and)g(only)h(if)e(they)i(con)m(tain)g
Fn(\000)p Fs(p)3456 5108 y Fj(0)3480 5145 y Fu(.)43 b(Supp)s(ose)0
5261 y Fn(\000)p Fs(p)33 b Fu(is)g(in)g Fs(l)i Fu(suc)m(h)f(cones.)44
b(Then)34 b Fs(z)1253 5276 y Fq(S)1304 5261 y Fu(\()p
Fs(p)p Fu(\))28 b(=)f Fs(l)e Fu(+)d Fs(k)s Fu(,)32 b(while)i
Fs(z)2125 5276 y Fq(S)2176 5261 y Fu(\()p Fs(p)2263 5225
y Fj(0)2286 5261 y Fu(\))28 b(=)f Fs(l)e Fu(+)d Fs(u)f
Fn(\000)i Fs(k)i Fn(\000)e Fu(\()p Fs(d)f Fn(\000)g Fu(1\).)p
eop end
%%Page: 6 6
TeXDict begin 6 5 bop 0 75 a Fl(6)536 b(ANTOINE)25 b(DEZA,)g(SUI)f
(HUANG,)h(T)-6 b(AMON)25 b(STEPHEN)h(AND)e(T)-6 b(AM)2823
56 y(\023)2813 75 y(AS)25 b(TERLAKY)100 274 y Fu(W)-8
b(e)36 b(conclude)h(that)f(giv)m(en)h(the)f(v)-5 b(alue)36
b(of)g Fs(z)1734 289 y Fq(S)1785 274 y Fu(\()p Fs(p)p
Fu(\))g(at)f(some)i(p)s(oin)m(t)f Fs(p)p Fu(,)g(w)m(e)h(can)f(in)h
(principle)g(compute)0 390 y Fs(z)45 405 y Fq(S)96 390
y Fu(\()p Fs(p)183 354 y Fj(0)206 390 y Fu(\))22 b(for)g(an)m(y)h
(other)f(p)s(oin)m(t)g Fs(p)1116 354 y Fj(0)1162 390
y Fu(b)m(y)h(tracing)f(a)g(path)g(from)g Fn(\000)p Fs(p)g
Fu(to)g Fn(\000)p Fs(p)2498 354 y Fj(0)2522 390 y Fu(,)i(and)e(seeing)h
(ho)m(w)g(eac)m(h)g(h)m(yp)s(erplane)0 506 y(generated)34
b(from)f(p)s(oin)m(ts)g(in)h Fs(U)39 b Fu(=)28 b Fs(S)g
Fn(n)22 b(f)p Fs(p)p Fn(g)33 b Fu(divides)i(the)e(p)s(oin)m(ts)h(of)e
Fs(U)10 b Fu(.)46 b(T)-8 b(o)33 b(do)g(this)h(formally)-8
b(,)33 b(w)m(e)h(need)0 623 y(a)39 b(top)s(ological)g(lemma)h(that)f
(sa)m(ys)i(w)m(e)f(can)g(alw)m(a)m(ys)h(dra)m(w)f(a)f(path)g(b)s(et)m
(w)m(een)j(t)m(w)m(o)e(p)s(oin)m(ts)g(on)f Fr(S)3641
586 y Fq(d)3721 623 y Fu(that)0 739 y(crosses)g(only)e(h)m(yp)s
(erplanes)i(from)e Fs(U)48 b Fu(\(as)37 b(opp)s(osed)h(to)e(passing)i
(through)f(cones)h(generated)g(b)m(y)g(few)m(er)0 855
y(than)31 b(\()p Fs(d)18 b Fn(\000)h Fu(1\))31 b(p)s(oin)m(ts\).)43
b(This)32 b(reduces)h(to)d(the)i(follo)m(wing)f(fact)f(whic)m(h)j(can)e
(b)s(e)g(pro)m(v)m(ed)h(using)g(algebraic)0 971 y(top)s(ology)-8
b(,)32 b(see)i(for)e(example)i([Mun84]:)0 1144 y FA(Lemma)40
b(3.3.)j Fp(The)35 b(spher)-5 b(e)35 b Fr(S)1171 1108
y Fq(d)1212 1144 y Fp(,)h(a)g Fu(\()p Fs(d)22 b Fn(\000)h
Fu(1\))36 b Fp(dimensional)e(manifold,)h(r)-5 b(emains)34
b(p)-5 b(ath)36 b(c)-5 b(onne)g(cte)g(d)35 b(after)0
1260 y(r)-5 b(emoving)34 b(\014nitely)g(many)h Fu(\()p
Fs(d)22 b Fn(\000)g Fu(3\))p Fp(-dimensional)33 b(manifolds.)0
1433 y Fu(3.3.)49 b FA(P)m(arit)m(y.)f Fu(The)h(v)-5
b(ariational)48 b(approac)m(h)h(to)f(computing)h Fs(z)2416
1448 y Fq(S)2467 1433 y Fu(\()p Fs(p)p Fu(\))g(explains)h(the)f(follo)m
(wing)f(parit)m(y)0 1549 y(phenomenon:)0 1721 y FA(Prop)s(osition)h
(3.4.)e Fp(F)-7 b(or)44 b(any)g(c)-5 b(olourful)44 b(c)-5
b(on\014gur)g(ation)44 b FA(S)g Fp(of)g Fu(\()p Fs(d)29
b Fu(+)g(1\))44 b Fp(p)-5 b(oints)44 b(in)g(e)-5 b(ach)44
b(of)g Fu(\()p Fs(d)28 b Fu(+)h(1\))0 1838 y Fp(c)-5
b(olours)36 b(in)h Fu(o)s(dd)g Fp(dimension)e Fs(d)h
Fp(and)h(any)f(p)-5 b(oint)37 b Fs(p)g Fp(with)f FA(S)h
Fp(and)g Fs(p)f Fp(in)h(gener)-5 b(al)36 b(p)-5 b(osition,)36
b(the)h(c)-5 b(olourful)0 1954 y(simplicial)33 b(depth)i(of)f
Fs(p)h Fp(with)g(r)-5 b(esp)g(e)g(ct)35 b(to)g FA(S)g
Fp(is)f Fu(ev)m(en)p Fp(.)100 2127 y Fu(The)25 b(authors)g(w)m(ere)h
(surprised)g(b)m(y)g(this)f(fact)f(while)i(exp)s(erimen)m(ting)h(with)e
(con\014gurations.)42 b(Ho)m(w)m(ev)m(er,)0 2243 y(it)j(is)g(easy)g(to)
g(explain)h(this)f(via)g(a)f(colourful)h(v)m(ersion)h(of)e(the)h(metho)
s(d)g(describ)s(ed)i(in)e(Section)g(3.2.)0 2359 y(Supp)s(ose)f(w)m(e)f
(b)s(egin)g(with)g(a)g(con\014guration)g FA(S)1806 2323
y Fo(0)1888 2359 y Fu(with)g(\()p Fs(d)29 b Fu(+)g(1\))42
b(p)s(oin)m(ts)h(in)g(eac)m(h)g(of)g(\()p Fs(d)28 b Fu(+)h(1\))42
b(colours)0 2475 y(clustered)i(near)f(the)f(North)h(P)m(ole)g(of)f
Fr(S)1522 2439 y Fq(d)1563 2475 y Fu(.)72 b(\(W)-8 b(e)43
b(remark)m(ed)h(in)e(Section)i(3.1)e(that)g(it)g(is)h(su\016cien)m(t)h
(to)0 2591 y(consider)37 b(con\014gurations)g(on)f(the)g(surface)h(of)e
Fr(S)1827 2555 y Fq(d)1868 2591 y Fu(\).)54 b(Then)37
b(w)m(e)g(can)f(mo)m(v)m(e)h(one)f(p)s(oin)m(t)g(at)g(a)g(time)g(from)0
2708 y(its)42 b(initial)g(p)s(osition)h(in)f FA(S)1003
2672 y Fo(0)1084 2708 y Fu(to)g(its)g(\014nal)g(p)s(osition)g(in)g
FA(S)g Fu(generating)h(a)e(sequence)k(of)c(con\014gurations)0
2827 y FA(S)62 2791 y Fo(0)102 2827 y Fs(;)17 b FA(S)208
2791 y Fo(1)247 2827 y Fs(;)g FA(S)353 2791 y Fo(2)393
2827 y Fs(;)g(:)g(:)g(:)e(;)i FA(S)673 2791 y Fo(\()p
Fq(d)p Fo(+1\))853 2767 y Fg(2)921 2827 y Fu(=)28 b FA(S)p
Fu(.)42 b(Clearly)31 b FA(depth)1773 2851 y Fh(S)1818
2832 y Fg(0)1857 2827 y Fu(\()p FA(0)p Fu(\))d(=)f(0.)43
b(As)30 b(w)m(e)g(mo)m(v)m(e)h(a)e(giv)m(en)i(p)s(oin)m(t)e
Fs(p)3399 2842 y Fq(i)3457 2827 y Fu(of)g(colour)g Fs(j)0
2943 y Fu(from)k(its)h(initial)f(p)s(osition)h(in)f FA(S)1199
2907 y Fo(0)1272 2943 y Fu(\(and)g FA(S)1562 2907 y Fq(i)1591
2943 y Fu(\))g(to)g(its)h(\014nal)f(p)s(osition)h(in)f
FA(S)h Fu(\(and)f FA(S)3009 2907 y Fq(i)p Fo(+1)3127
2943 y Fu(\),)h(w)m(e)g(need)h(only)e(to)0 3060 y(kno)m(w)e(what)e
(happ)s(ens)i(when)g(the)e(an)m(tip)s(o)s(de)h Fn(\000)p
Fs(p)1815 3075 y Fq(i)1873 3060 y Fu(crosses)h(colourful)f(h)m(yp)s
(erplanes)i(de\014ned)f(b)m(y)f(a)f(set)h(of)0 3176 y(\()p
Fs(d)12 b Fn(\000)g Fu(1\))27 b(p)s(oin)m(ts)h(of)f(\()p
Fs(d)12 b Fn(\000)g Fu(1\))27 b(colours,)i(and)f(not)f(of)g(colour)h
Fs(j)6 b Fu(.)42 b(Suc)m(h)28 b(a)g(colourful)f(h)m(yp)s(erplane)i
Fs(H)35 b Fu(will)29 b(miss)0 3292 y(only)f(one)h(other)f(colour,)h
Fs(j)996 3256 y Fj(0)1019 3292 y Fu(.)42 b(There)29 b(will)g(b)s(e)f
Fs(k)j Fu(p)s(oin)m(ts)d(of)g(colour)g Fs(j)2484 3256
y Fj(0)2535 3292 y Fu(on)g(one)g(side)h(of)e Fs(H)8 b
Fu(,)29 b(and)f(\()p Fs(d)13 b Fu(+)g(1)g Fn(\000)g Fs(k)s
Fu(\))0 3408 y(on)32 b(the)h(other)f(side.)44 b(Here)33
b(w)m(e)g(are)f(assuming)i(that)e(the)g(p)s(oin)m(ts)h(from)f
FA(S)g Fu(are)g(in)h(general)f(p)s(osition,)h(but)0 3524
y(w)m(e)43 b(can)f(argue)g(b)m(y)g(con)m(tin)m(uit)m(y)i(that)e(this)g
(assumption)h(is)f(not)g(necessary)-8 b(.)73 b(As)42
b Fn(\000)p Fs(p)3233 3539 y Fq(i)3304 3524 y Fu(crosses)h
Fs(H)50 b Fu(the)0 3641 y(n)m(um)m(b)s(er)31 b(of)e(simplicial)i(cones)
g(con)m(taining)g Fn(\000)p Fs(p)1747 3656 y Fq(i)1805
3641 y Fu(generated)f(b)m(y)h(p)s(oin)m(ts)f(from)g Fs(H)37
b Fu(and)29 b(a)h(p)s(oin)m(t)g(of)f(colour)0 3757 y
Fs(j)46 3721 y Fj(0)102 3757 y Fu(c)m(hanges)34 b(from)e
Fs(k)k Fu(to)c(\()p Fs(d)22 b Fu(+)g(1)g Fn(\000)g Fs(k)s
Fu(\).)44 b(As)33 b(long)f(as)h(\()p Fs(d)22 b Fu(+)g(1\))32
b(is)h(ev)m(en,)h(the)f(parit)m(y)h(do)s(esn't)f(c)m(hange.)100
3873 y(Examining)g(this)h(pro)s(of,)d(w)m(e)j(can)f(see)h(that)e(Prop)s
(osition)h(3.4)f(can)h(b)s(e)g(generalized:)0 4046 y
FA(Theorem)41 b(3.5.)i Fp(If)60 b FA(S)32 b Fu(=)f Fn(f)p
Fs(S)1134 4061 y Fo(1)1173 4046 y Fs(;)17 b(S)1277 4061
y Fo(2)1316 4046 y Fs(;)g(:)g(:)g(:)f(;)h(S)1595 4061
y Fq(r)1633 4046 y Fn(g)37 b Fp(is)f(a)h Fs(d)p Fp(-dimensional)e(c)-5
b(olourful)37 b(c)-5 b(on\014gur)g(ation)36 b(of)g(p)-5
b(oints)0 4162 y(and)42 b(for)g(e)-5 b(ach)42 b Fs(i)h
Fu(=)f(1)p Fs(;)17 b Fu(2)p Fs(;)g(:)g(:)g(:)e(;)i(r)45
b Fp(we)d(have)g Fn(j)p Fs(S)1702 4177 y Fq(i)1730 4162
y Fn(j)g Fp(even,)i(and)e Fs(p)g Fp(is)h(and)f(any)g(p)-5
b(oint)43 b Fs(p)f Fp(with)h FA(S)g Fp(and)f Fs(p)g Fp(in)0
4278 y(gener)-5 b(al)34 b(p)-5 b(osition,)34 b(then)h(the)g(c)-5
b(olourful)34 b(simplicial)g(depth)g(of)h Fs(p)g Fp(with)f(r)-5
b(esp)g(e)g(ct)35 b(to)g FA(S)g Fp(is)g(also)f(even.)100
4451 y Fu(F)-8 b(or)38 b(mono)s(c)m(hrome)i(depth,)h(as)e(w)m(e)h(mo)m
(v)m(e)g(p)s(oin)m(t)g Fs(p)e Fu(around)h Fr(S)2448 4415
y Fq(d)2528 4451 y Fu(w)m(e)h(need)g(to)f(consider)h(all)f(p)s(ossible)
0 4567 y(h)m(yp)s(erplanes)c(formed)e(from)f Fs(S)c Fn(n)22
b(f)p Fs(p)p Fn(g)p Fu(.)43 b(Using)33 b(the)g(same)h(reasoning)f(as)f
(Theorem)i(3.5)e(w)m(e)i(get:)0 4740 y FA(Theorem)i(3.6.)41
b Fp(If)33 b Fs(S)40 b Fp(is)33 b(a)g(set)h(of)f Fs(n)h
Fp(p)-5 b(oints)33 b(in)g Fr(R)1906 4703 y Fq(d)1947
4740 y Fp(,)g(and)g Fs(n)20 b Fn(\000)f Fs(d)34 b Fp(is)f(even,)g(and)g
Fs(p)g Fp(is)h(a)f(p)-5 b(oint)33 b(such)h(that)0 4856
y Fs(S)28 b Fn([)22 b(f)p Fs(p)p Fn(g)35 b Fp(is)g(in)f(gener)-5
b(al)34 b(p)-5 b(osition,)34 b(then)h(the)g(simplicial)e(depth)i(of)f
Fs(p)h Fp(with)g(r)-5 b(esp)g(e)g(ct)34 b(to)h Fs(S)41
b Fp(is)35 b(even.)0 5028 y(R)-5 b(emark)58 b Fu(3.7)p
Fp(.)49 b Fu(The)f(v)-5 b(ariational)46 b(approac)m(h)h(suggested)i(in)
e(Section)h(3.2)f(has)g(app)s(eared)g(in)h(v)-5 b(arious)0
5145 y(guises)30 b(in)f(discussions)i(of)e(mono)s(c)m(hrome)g
(simplicial)h(depth.)44 b(In)29 b(particular,)g(it)g(underlies)i(man)m
(y)e(of)g(the)0 5261 y(algorithms)34 b(suggested)i(for)d(computing)i
(mono)s(c)m(hrome)g(simplicial)h(depth.)49 b(Sev)m(eral)35
b(suc)m(h)h(algorithms)p eop end
%%Page: 7 7
TeXDict begin 7 6 bop 1304 71 a Fl(COLOURFUL)32 b(SIMPLICIAL)g(DEPTH)
1266 b(7)0 274 y Fu(ha)m(v)m(e)50 b(b)s(een)f(prop)s(osed)g(recen)m
(tly)-8 b(,)54 b(see)c(for)e(example)h(the)g(discussion)i(in)e([Alo04)o
(].)91 b(Man)m(y)50 b(of)e(these)0 390 y(fo)s(cus)41
b(on)f(the)h(2-dimensional)g(problem,)i([GSW92])d(and)h([CO01])f(use)h
(v)-5 b(ariational)40 b(ideas)i(in)e(3-)g(and)0 506 y(4-dimensional)33
b(algorithms.)100 623 y(F)-8 b(or)38 b(this)i(reason,)h(w)m(e)f(b)s
(eliev)m(ed)i(that)d(Theorem)h(3.6)f(existed)i(as)e(folklore)h(for)e
(some)i(time.)64 b(Bak)m(er)0 739 y(remarks)28 b(on)g(the)f(t)m(w)m
(o-dimensional)i(v)m(ersion)g(in)f(a)e(recreational)i(mathematics)h
(note)e([Bak78],)i(but)e(this)0 855 y(fact,)32 b(whic)m(h)h(impressed)g
(the)f(authors)g(with)g(its)g(simple)h(elegance,)g(seems)g(curiously)g
(neglected)g(in)f(the)0 971 y(literature.)52 b(W)-8 b(e)36
b(sp)s(eculate)h(that)e(one)h(reason)f(for)g(this)h(is)g(that)f(in)h
(statistics)h(the)f(fo)s(cus)f(has)h(b)s(een)g(on)0 1087
y(computing)31 b(the)f(depth)h(of)f(the)g(sample)i(p)s(oin)m(ts)e
(themselv)m(es,)k(whic)m(h)e(are)e(not)g(in)g(general)h(p)s(osition)f
(and)0 1204 y(do)i(not)h(retain)g(nice)g(parit)m(y)g(conditions.)0
1383 y(3.4.)49 b FA(Con\014gurations)40 b(with)e(Small)i(Minimal)h
(Colourful)f(Depth.)49 b Fu(W)-8 b(e)34 b(no)m(w)g(describ)s(e)i(ho)m
(w)e(to)0 1499 y(build)29 b(a)f(colourful)g(con\014guration)h
FA(S)1370 1463 y Fj(\000)1457 1499 y Fu(that)f(con)m(tains)i
FA(0)e Fu(in)g(its)h(core,)g(but)g(where)g(only)g Fs(d)3310
1463 y Fo(2)3363 1499 y Fu(+)13 b(1)28 b(colourful)0
1615 y(simplices)34 b(con)m(tain)e FA(0)p Fu(.)44 b(Our)31
b(strategy)i(is)f(to)f(\014x)i(the)f(\014rst)g Fs(d)f
Fu(colourful)h(sets)h Fs(S)2919 1574 y Fj(\000)2913 1640
y Fo(1)2978 1615 y Fs(;)17 b(S)3088 1574 y Fj(\000)3082
1640 y Fo(2)3146 1615 y Fs(;)g(:)g(:)g(:)f(;)h(S)3431
1574 y Fj(\000)3425 1643 y Fq(d)3521 1615 y Fu(and)32
b(then)0 1733 y(consider)40 b(p)s(ossible)f(placemen)m(ts)i(of)d(\()p
Fs(d)25 b Fu(+)h(1\))38 b(p)s(oin)m(ts)h Fs(p)2072 1748
y Fo(1)2112 1733 y Fs(;)17 b(p)2205 1748 y Fo(2)2244
1733 y Fs(;)g(:)g(:)g(:)f(;)h(p)2512 1748 y Fq(d)p Fo(+1)2680
1733 y Fu(to)38 b(form)g Fs(S)3107 1691 y Fj(\000)3101
1760 y Fq(d)p Fo(+1)3232 1733 y Fu(.)60 b(W)-8 b(e)39
b(will)g(place)0 1858 y(the)34 b(p)s(oin)m(ts)f(from)g
Fs(S)759 1817 y Fj(\000)753 1882 y Fo(1)841 1858 y Fn([)23
b Fs(S)996 1817 y Fj(\000)990 1882 y Fo(2)1077 1858 y
Fn([)g Fs(:)17 b(:)g(:)22 b Fn([)h Fs(S)1458 1817 y Fj(\000)1452
1886 y Fq(d)1550 1858 y Fu(on)33 b(the)h(sphere)g Fr(S)2214
1822 y Fq(d)2288 1858 y Fu(in)g(suc)m(h)g(a)f(w)m(a)m(y)i(that)e(some)h
(regions)f(of)g Fr(S)3859 1822 y Fq(d)0 1975 y Fu(are)g(sparsely)h(co)m
(v)m(ered)g(b)m(y)g(simplices)h(from)d Fs(S)1729 1934
y Fj(\000)1723 2000 y Fo(1)1810 1975 y Fn([)23 b Fs(S)1965
1934 y Fj(\000)1959 2000 y Fo(2)2046 1975 y Fn([)f Fs(:)17
b(:)g(:)22 b Fn([)g Fs(S)2425 1934 y Fj(\000)2419 2003
y Fq(d)2484 1975 y Fu(.)100 2094 y(W)-8 b(e)37 b(b)s(egin)f(b)m(y)i
(\014xing)f Fs(\017)e Fu(=)1197 2054 y Fo(1)p 1144 2071
143 4 v 1144 2128 a(100)p Fq(d)1296 2094 y Fu(.)55 b(W)-8
b(e)37 b(will)h(place)f(the)g(p)s(oin)m(ts)g(from)f FA(S)2757
2057 y Fj(\000)2853 2094 y Fu(in)h(three)g(lo)s(cations)g(on)f
Fr(S)3832 2057 y Fq(d)3873 2094 y Fu(.)0 2218 y(The)29
b(\014rst)f(on)g(the)g Fp(T)-7 b(r)i(opic)29 b(of)i(Capric)-5
b(orn)p Fu(,)27 b(whic)m(h)j(w)m(e)f(de\014ne)g(to)e(b)s(e)h(the)g(set)
h(of)e(p)s(oin)m(ts)i(on)f Fr(S)3406 2182 y Fq(d)3474
2218 y Fu(whose)h Fs(d)p Fu(th)0 2335 y(co)s(ordinate)36
b(is)h Fn(\000)p Fu(2)p Fs(\017)p Fu(.)54 b(The)37 b(second)g(is)g(on)f
(the)g Fp(T)-7 b(r)i(opic)37 b(of)g(Canc)-5 b(er)p Fu(,)36
b(whose)i Fs(d)p Fu(th)d(co)s(ordinate)h(is)h Fs(\017)p
Fu(.)54 b(The)0 2451 y(t)m(w)m(o)32 b(tropics)f(are)g(top)s(ologically)
g(copies)h(of)f Fr(S)1686 2415 y Fq(d)p Fj(\000)p Fo(1)1817
2451 y Fu(,)g(but)g(unlik)m(e)i(their)e(namesak)m(es)j(they)e(are)f
(not)g(equally)0 2567 y(spaced)e(from)f(the)g(equator.)43
b(The)29 b(\014nal)f(region)g(is)h(the)f Fp(p)-5 b(olar)30
b(r)-5 b(e)g(gion)27 b Fu(of)h(p)s(oin)m(ts)h(in)f Fr(S)3128
2531 y Fq(d)3196 2567 y Fu(whic)m(h)i(are)e(within)0
2683 y Fs(\017)33 b Fu(of)f(the)h(North)f(P)m(ole)i Fs(p)900
2698 y Fo(north)1100 2683 y Fu(=)28 b(\(0)p Fs(;)17 b
Fu(0)p Fs(;)g(:)g(:)g(:)e(;)i Fu(0)p Fs(;)g Fu(1\).)988
4114 y @beginspecial 0 @llx 0 @lly 436 @urx 289 @ury
1530 @rhi @setspecial
%%BeginDocument: regions.eps
%!PS-Adobe-2.0 EPSF-2.0
%%Title: regions.eps
%%Creator: fig2dev Version 3.2 Patchlevel 3c
%%CreationDate: Fri May 13 15:12:27 2005
%%For: tamon@birkhoff (Tamon Stephen,TTCA)
%%BoundingBox: 0 0 436 289
%%Magnification: 1.0000
%%EndComments
/$F2psDict 200 dict def
$F2psDict begin
$F2psDict /mtrx matrix put
/col-1 {0 setgray} bind def
/col0 {0.000 0.000 0.000 srgb} bind def
/col1 {0.000 0.000 1.000 srgb} bind def
/col2 {0.000 1.000 0.000 srgb} bind def
/col3 {0.000 1.000 1.000 srgb} bind def
/col4 {1.000 0.000 0.000 srgb} bind def
/col5 {1.000 0.000 1.000 srgb} bind def
/col6 {1.000 1.000 0.000 srgb} bind def
/col7 {1.000 1.000 1.000 srgb} bind def
/col8 {0.000 0.000 0.560 srgb} bind def
/col9 {0.000 0.000 0.690 srgb} bind def
/col10 {0.000 0.000 0.820 srgb} bind def
/col11 {0.530 0.810 1.000 srgb} bind def
/col12 {0.000 0.560 0.000 srgb} bind def
/col13 {0.000 0.690 0.000 srgb} bind def
/col14 {0.000 0.820 0.000 srgb} bind def
/col15 {0.000 0.560 0.560 srgb} bind def
/col16 {0.000 0.690 0.690 srgb} bind def
/col17 {0.000 0.820 0.820 srgb} bind def
/col18 {0.560 0.000 0.000 srgb} bind def
/col19 {0.690 0.000 0.000 srgb} bind def
/col20 {0.820 0.000 0.000 srgb} bind def
/col21 {0.560 0.000 0.560 srgb} bind def
/col22 {0.690 0.000 0.690 srgb} bind def
/col23 {0.820 0.000 0.820 srgb} bind def
/col24 {0.500 0.190 0.000 srgb} bind def
/col25 {0.630 0.250 0.000 srgb} bind def
/col26 {0.750 0.380 0.000 srgb} bind def
/col27 {1.000 0.500 0.500 srgb} bind def
/col28 {1.000 0.630 0.630 srgb} bind def
/col29 {1.000 0.750 0.750 srgb} bind def
/col30 {1.000 0.880 0.880 srgb} bind def
/col31 {1.000 0.840 0.000 srgb} bind def
/col32 {0.255 0.255 0.255 srgb} bind def
/col33 {0.525 0.510 0.525 srgb} bind def
/col34 {0.745 0.765 0.745 srgb} bind def
/col35 {0.875 0.890 0.875 srgb} bind def
/col36 {0.525 0.510 0.525 srgb} bind def
/col37 {0.745 0.765 0.745 srgb} bind def
/col38 {0.875 0.890 0.875 srgb} bind def
/col39 {0.286 0.271 0.286 srgb} bind def
/col40 {0.286 0.271 0.286 srgb} bind def
/col41 {0.557 0.557 0.557 srgb} bind def
/col42 {0.620 0.000 0.000 srgb} bind def
/col43 {0.620 0.000 0.000 srgb} bind def
/col44 {0.557 0.557 0.557 srgb} bind def
/col45 {0.255 0.255 0.255 srgb} bind def
/col46 {0.557 0.557 0.557 srgb} bind def
/col47 {0.255 0.255 0.255 srgb} bind def
/col48 {0.557 0.557 0.557 srgb} bind def
/col49 {0.255 0.255 0.255 srgb} bind def
/col50 {0.557 0.557 0.557 srgb} bind def
/col51 {0.255 0.255 0.255 srgb} bind def
/col52 {0.557 0.557 0.557 srgb} bind def
/col53 {0.255 0.255 0.255 srgb} bind def
/col54 {0.557 0.557 0.557 srgb} bind def
/col55 {0.255 0.255 0.255 srgb} bind def
/col56 {0.557 0.557 0.557 srgb} bind def
/col57 {0.255 0.255 0.255 srgb} bind def
/col58 {0.557 0.557 0.557 srgb} bind def
/col59 {0.255 0.255 0.255 srgb} bind def
/col60 {0.557 0.557 0.557 srgb} bind def
/col61 {0.255 0.255 0.255 srgb} bind def
/col62 {0.557 0.557 0.557 srgb} bind def
/col63 {0.255 0.255 0.255 srgb} bind def
/col64 {0.557 0.557 0.557 srgb} bind def
/col65 {0.255 0.255 0.255 srgb} bind def
/col66 {0.557 0.557 0.557 srgb} bind def
/col67 {0.255 0.255 0.255 srgb} bind def
/col68 {0.557 0.557 0.557 srgb} bind def
/col69 {0.255 0.255 0.255 srgb} bind def
/col70 {0.557 0.557 0.557 srgb} bind def
/col71 {0.255 0.255 0.255 srgb} bind def
/col72 {0.557 0.557 0.557 srgb} bind def
/col73 {0.255 0.255 0.255 srgb} bind def
/col74 {0.557 0.557 0.557 srgb} bind def
/col75 {0.255 0.255 0.255 srgb} bind def
/col76 {0.557 0.557 0.557 srgb} bind def
/col77 {0.255 0.255 0.255 srgb} bind def
/col78 {0.557 0.557 0.557 srgb} bind def
/col79 {0.255 0.255 0.255 srgb} bind def
/col80 {0.745 0.765 0.745 srgb} bind def
/col81 {0.412 0.427 0.412 srgb} bind def
/col82 {0.745 0.765 0.745 srgb} bind def
/col83 {0.412 0.427 0.412 srgb} bind def
/col84 {0.286 0.271 0.286 srgb} bind def
/col85 {0.557 0.557 0.557 srgb} bind def
/col86 {0.412 0.427 0.412 srgb} bind def
/col87 {0.557 0.557 0.557 srgb} bind def
/col88 {0.443 0.443 0.443 srgb} bind def
/col89 {0.682 0.682 0.682 srgb} bind def
/col90 {0.188 0.188 0.188 srgb} bind def
/col91 {0.588 0.573 0.588 srgb} bind def
/col92 {0.443 0.443 0.443 srgb} bind def
/col93 {0.349 0.333 0.349 srgb} bind def
/col94 {0.682 0.698 0.682 srgb} bind def
/col95 {0.745 0.765 0.745 srgb} bind def
/col96 {0.286 0.271 0.286 srgb} bind def
/col97 {0.412 0.427 0.412 srgb} bind def
/col98 {0.286 0.271 0.286 srgb} bind def
/col99 {0.412 0.427 0.412 srgb} bind def
/col100 {0.745 0.765 0.745 srgb} bind def
/col101 {0.412 0.427 0.412 srgb} bind def
/col102 {0.286 0.271 0.286 srgb} bind def
/col103 {0.745 0.765 0.745 srgb} bind def
/col104 {0.412 0.427 0.412 srgb} bind def
/col105 {0.745 0.765 0.745 srgb} bind def
/col106 {0.286 0.271 0.286 srgb} bind def
/col107 {0.557 0.557 0.557 srgb} bind def
/col108 {0.875 0.890 0.937 srgb} bind def
/col109 {0.588 0.588 0.620 srgb} bind def
/col110 {0.843 0.859 0.843 srgb} bind def
/col111 {0.620 0.635 0.714 srgb} bind def
/col112 {0.620 0.000 0.000 srgb} bind def
/col113 {0.937 0.937 0.937 srgb} bind def
/col114 {0.875 0.890 0.875 srgb} bind def
/col115 {0.525 0.682 1.000 srgb} bind def
/col116 {0.443 0.443 1.000 srgb} bind def

end
save
newpath 0 293 moveto 0 0 lineto 436 0 lineto 436 293 lineto closepath clip newpath
-141.0 594.0 translate
1 -1 scale

/cp {closepath} bind def
/ef {eofill} bind def
/gr {grestore} bind def
/gs {gsave} bind def
/sa {save} bind def
/rs {restore} bind def
/l {lineto} bind def
/m {moveto} bind def
/rm {rmoveto} bind def
/n {newpath} bind def
/s {stroke} bind def
/sh {show} bind def
/slc {setlinecap} bind def
/slj {setlinejoin} bind def
/slw {setlinewidth} bind def
/srgb {setrgbcolor} bind def
/rot {rotate} bind def
/sc {scale} bind def
/sd {setdash} bind def
/ff {findfont} bind def
/sf {setfont} bind def
/scf {scalefont} bind def
/sw {stringwidth} bind def
/tr {translate} bind def
/tnt {dup dup currentrgbcolor
  4 -2 roll dup 1 exch sub 3 -1 roll mul add
  4 -2 roll dup 1 exch sub 3 -1 roll mul add
  4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb}
  bind def
/shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul
  4 -2 roll mul srgb} bind def
 /DrawEllipse {
	/endangle exch def
	/startangle exch def
	/yrad exch def
	/xrad exch def
	/y exch def
	/x exch def
	/savematrix mtrx currentmatrix def
	x y tr xrad yrad sc 0 0 1 startangle endangle arc
	closepath
	savematrix setmatrix
	} def

/$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def
/$F2psEnd {$F2psEnteredState restore end} def

$F2psBegin
%%Page: 1 1
10 setmiterlimit
 0.06000 0.06000 sc
%
% Fig objects follow
%
15.000 slw
% Ellipse
n 5400 7950 2025 300 0 360 DrawEllipse gs col0 s gr

% Polyline
n 3300 7575 m 7500 7575 l 7500 7950 l 3300 7950 l
 cp gs col7 1.00 shd ef gr gs col7 s gr 
% Ellipse
n 5400 7500 2100 300 0 360 DrawEllipse gs col0 s gr

% Ellipse
n 5407 5405 480 300 0 360 DrawEllipse gs col0 s gr

% Polyline
n 4785 5040 m 5970 5040 l 5970 5445 l 4785 5445 l
 cp gs col7 1.00 shd ef gr gs col7 s gr 
% Polyline
7.500 slw
n 3225 7125 m 7500 7125 l 7500 7500 l 3225 7500 l
 cp gs col7 1.00 shd ef gr gs col7 s gr 
15.000 slw
% Ellipse
n 5400 7260 2100 300 0 360 DrawEllipse gs col0 s gr

% Polyline
n 3225 6915 m 7545 6915 l 7545 7275 l 3225 7275 l
 cp gs col7 1.00 shd ef gr gs col7 s gr 
7.500 slw
 [60] 0 sd
% Ellipse
n 5423 7267 2100 300 0 360 DrawEllipse gs col0 s gr
 [] 0 sd
% Polyline
 [60] 0 sd
n 7500 7200 m 7650 7200 l 7650 7350 l 7500 7350 l
 cp gs col7 1.00 shd ef gr gs col7 s gr  [] 0 sd
% Polyline
gs  clippath
3570 7665 m 3630 7665 l 3630 7573 l 3600 7641 l 3570 7573 l cp
3630 7385 m 3570 7385 l 3570 7476 l 3600 7409 l 3630 7476 l cp
eoclip
n 3600 7400 m
 3600 7650 l gs col0 s gr gr

% arrowhead
n 3630 7476 m 3600 7409 l 3570 7476 l 3600 7499 l 3630 7476 l 
 cp gs 0.00 setgray ef gr  col0 s
% arrowhead
n 3570 7573 m 3600 7641 l 3630 7573 l 3600 7551 l 3570 7573 l 
 cp gs 0.00 setgray ef gr  col0 s
 [60] 0 sd
% Ellipse
n 5400 7950 2025 300 0 360 DrawEllipse gs col0 s gr
 [] 0 sd
/Times-Italic ff 240.00 scf sf
6180 5460 m
gs 1 -1 sc (North polar region) col0 sh gr
/Times-Italic ff 240.00 scf sf
2355 7635 m
gs 1 -1 sc (Equator) col0 sh gr
/Times-Italic ff 240.00 scf sf
7635 7380 m
gs 1 -1 sc (Tropic of Cancer) col0 sh gr
/Times-Italic ff 240.00 scf sf
7590 8085 m
gs 1 -1 sc (Tropic of Capricorn) col0 sh gr
/Symbol ff 180.00 scf sf
3450 7575 m
gs 1 -1 sc (e) col0 sh gr
/Times-Italic ff 150.00 scf sf
5565 5295 m
gs 1 -1 sc (north) col0 sh gr
% Polyline
gs  clippath
5370 8265 m 5430 8265 l 5430 8173 l 5400 8241 l 5370 8173 l cp
5430 7760 m 5370 7760 l 5370 7851 l 5400 7784 l 5430 7851 l cp
eoclip
n 5400 7775 m
 5400 8250 l gs col0 s gr gr

% arrowhead
n 5430 7851 m 5400 7784 l 5370 7851 l 5400 7874 l 5430 7851 l 
 cp gs 0.00 setgray ef gr  col0 s
% arrowhead
n 5370 8173 m 5400 8241 l 5430 8173 l 5400 8151 l 5370 8173 l 
 cp gs 0.00 setgray ef gr  col0 s
/Times-Italic ff 150.00 scf sf
5580 9885 m
gs 1 -1 sc (south) col0 sh gr
/Times-Italic ff 240.00 scf sf
5490 5220 m
gs 1 -1 sc (p) col0 sh gr
/Symbol ff 180.00 scf sf
5220 8085 m
gs 1 -1 sc (e) col0 sh gr
/Times-Italic ff 180.00 scf sf
5100 8100 m
gs 1 -1 sc (2) col0 sh gr
15.000 slw
% Ellipse
n 5400 7500 2100 2100 0 360 DrawEllipse gs col0 s gr

7.500 slw
% Ellipse
n 5400 9600 75 75 0 360 DrawEllipse gs 0.00 setgray ef gr gs col0 s gr

% Ellipse
n 5400 5400 75 75 0 360 DrawEllipse gs 0.00 setgray ef gr gs col0 s gr

 [60] 0 sd
% Ellipse
n 5400 7500 2100 300 0 360 DrawEllipse gs col0 s gr
 [] 0 sd
/Times-Italic ff 240.00 scf sf
5505 9810 m
gs 1 -1 sc (p) col0 sh gr
$F2psEnd
rs

%%EndDocument
 @endspecial 307 4330 a Ft(Figure)37 b(1.)49 b Fu(3-dimensional)33
b(illustration)g(of)f(the)h(regions)g(used)h(in)f(constructing)h
FA(S)3507 4294 y Fj(\000)3566 4330 y Fu(.)100 4570 y(No)m(w)f(let's)g
(\014x)g(the)g(p)s(ositions)h(of)e(the)h(p)s(oin)m(ts)g
Fn(f)p Fs(x)1922 4585 y Fo(1)1962 4570 y Fs(;)17 b(x)2061
4585 y Fo(2)2100 4570 y Fs(;)g(:)g(:)g(:)f(;)h(x)2374
4585 y Fq(d)p Fo(+1)2505 4570 y Fn(g)27 b(2)h Fs(S)2742
4529 y Fj(\000)2736 4595 y Fo(1)2801 4570 y Fu(.)44 b(T)-8
b(ak)m(e:)348 4747 y Fs(x)403 4762 y Fo(1)470 4747 y
Fu(=)28 b(\()612 4660 y Fn(p)p 695 4660 299 4 v 87 x
Fu(1)22 b Fn(\000)g Fu(4)p Fs(\017)953 4718 y Fo(2)993
4747 y Fs(;)17 b Fu(0)p Fs(;)g Fu(0)p Fs(;)g(:)g(:)g(:)e(;)i
Fu(0)p Fs(;)g Fn(\000)p Fu(2)p Fs(\017)p Fu(\))227 b(and)h
Fs(x)2360 4762 y Fo(2)2428 4747 y Fu(=)27 b(\()p Fn(\000)2646
4660 y(p)p 2730 4660 250 4 v 2730 4747 a Fu(1)21 b Fn(\000)i
Fs(\017)2939 4718 y Fo(2)2979 4747 y Fs(;)17 b Fu(0)p
Fs(;)g Fu(0)p Fs(;)g(:)g(:)g(:)e(;)i Fu(0)p Fs(;)g(\017)p
Fu(\))0 4912 y(Note)32 b(that)f(the)h(line)g(segmen)m(t)i(b)s(et)m(w)m
(een)f Fs(x)1602 4927 y Fo(1)1674 4912 y Fu(and)e Fs(x)1917
4927 y Fo(2)1989 4912 y Fu(passes)i(just)f(b)s(elo)m(w)g(the)g(origin)g
(in)g(the)g(sense)h(that)0 5028 y(it)27 b(con)m(tains)h(a)f(p)s(oin)m
(t)g(whose)h(\014rst)f(\()p Fs(d)11 b Fn(\000)g Fu(1\))26
b(co)s(ordinates)i(are)f(0,)g(and)g(whose)i Fs(d)p Fu(th)d(co)s
(ordinate)h(is)h(negativ)m(e)0 5145 y(\(and)36 b(small\).)56
b(W)-8 b(e)36 b(no)m(w)h(place)g(the)g(remaining)g(p)s(oin)m(ts)g
Fs(x)2188 5160 y Fo(3)2228 5145 y Fs(;)17 b(:)g(:)g(:)f(;)h(x)2502
5160 y Fq(d)p Fo(+1)2669 5145 y Fu(in)36 b(the)h(p)s(olar)f(region)g
(in)g(suc)m(h)i(a)0 5261 y(w)m(a)m(y)j(as)e(to)g(ensure)i(that)f
FA(0)f Fn(2)h Fu(in)m(t\(con)m(v)s(\()p Fs(S)1643 5220
y Fj(\000)1637 5285 y Fo(1)1701 5261 y Fu(\)\).)64 b(F)-8
b(or)39 b Fs(d)g Fu(=)g(2)g(w)m(e)i(can)f(do)f(this)h(b)m(y)g(placing)g
Fs(x)3559 5276 y Fo(3)3638 5261 y Fu(at)g(the)p eop end
%%Page: 8 8
TeXDict begin 8 7 bop 0 75 a Fl(8)536 b(ANTOINE)25 b(DEZA,)g(SUI)f
(HUANG,)h(T)-6 b(AMON)25 b(STEPHEN)h(AND)e(T)-6 b(AM)2823
56 y(\023)2813 75 y(AS)25 b(TERLAKY)0 274 y Fu(North)g(P)m(ole.)42
b(F)-8 b(or)25 b Fs(d)i Fn(\025)h Fu(3)e(w)m(e)g(can)g(place)g(the)g(p)
s(oin)m(ts)g(on)f(the)h(section)h(of)e(the)g(Arctic)i(Circle)f(\(p)s
(oin)m(ts)g(with)0 390 y(distance)33 b Fs(\017)f Fu(to)f(the)h(North)f
(P)m(ole\))i(with)f(zero)g(initial)f(co)s(ordinate.)44
b(T)-8 b(op)s(ologically)31 b(the)h(Arctic)h(Circle)f(is)0
506 y(a)g(cop)m(y)i(of)e Fr(S)475 470 y Fq(d)p Fj(\000)p
Fo(2)606 506 y Fu(;)g(w)m(e)i(can)f(tak)m(e)g Fs(x)1254
521 y Fo(3)1294 506 y Fs(;)17 b(:)g(:)g(:)f(;)h(x)1568
521 y Fq(d)p Fo(+1)1731 506 y Fu(to)32 b(b)s(e)h(the)g(v)m(ertices)i
(of)d(a)g(regular)g(simplex)j(inscrib)s(ed)f(on)0 623
y(this)f(sphere.)100 739 y(The)41 b(p)s(oin)m(ts)g(of)f(colours)h(2)p
Fs(;)17 b Fu(3)p Fs(;)g(:)g(:)g(:)e(;)i(d)40 b Fu(are)h(c)m(hosen)h
(similarly)-8 b(.)68 b(The)42 b(\014rst)f(p)s(oin)m(ts)g(from)f(eac)m
(h)h(of)g(the)0 855 y Fs(d)k Fu(colours)h(are)g(arranged)g(in)f(a)h
(regular)f(simplex)j(on)d(Capricorn.)84 b(The)46 b(remaining)g(p)s(oin)
m(ts)h(in)f(the)0 971 y(same)33 b(relativ)m(e)h(p)s(osition)e(to)g(the)
h(\014rst)g(p)s(oin)m(t,)g(so)f(that)g(eac)m(h)h Fs(S)2347
930 y Fj(\000)2341 997 y Fq(i)2439 971 y Fu(is)f(a)g(rotation)g(of)g
Fs(S)3168 930 y Fj(\000)3162 996 y Fo(1)3259 971 y Fu(around)g(the)h
Fs(d)p Fu(th)0 1087 y(co)s(ordinate)41 b(axis.)68 b(In)41
b(particular,)i(for)d(eac)m(h)h Fs(i)h Fu(=)f(1)p Fs(;)17
b Fu(2)p Fs(;)g(:)g(:)g(:)e(;)i(d)p Fu(,)42 b(the)f(second)h(p)s(oin)m
(t)e(of)g Fs(S)3367 1046 y Fj(\000)3361 1113 y Fq(i)3467
1087 y Fu(will)h(lie)g(on)0 1204 y(Cancer)34 b(and)e(the)h(\014nal)g
(\()p Fs(d)22 b Fn(\000)g Fu(1\))33 b(p)s(oin)m(ts)g(will)g(lie)g(in)g
(the)g(p)s(olar)f(region.)100 1320 y(W)-8 b(e)29 b(\014nish)h(our)f
(construction)h(b)m(y)f(considering)i(p)s(ossible)f(placemen)m(ts)h(of)
d(the)i(p)s(oin)m(ts)f Fs(p)3355 1335 y Fo(1)3395 1320
y Fs(;)17 b(:)g(:)g(:)e(;)i(p)3662 1335 y Fq(d)p Fo(+1)3821
1320 y Fu(of)0 1436 y Fs(S)66 1395 y Fj(\000)60 1464
y Fq(d)p Fo(+1)191 1436 y Fu(.)42 b(W)-8 b(e)30 b(w)m(an)m(t)h(to)e
(place)i(the)f Fs(p)1238 1451 y Fq(i)1266 1436 y Fu('s)g(in)g(suc)m(h)h
(a)e(w)m(a)m(y)i(that)f(their)g(an)m(tip)s(o)s(des)g(\(the)g
Fn(\000)p Fs(p)3169 1451 y Fq(i)3198 1436 y Fu('s\))g(are)g(con)m
(tained)0 1555 y(in)j(few)g(colourful)g(simplicial)h(cones)f(generated)
h(from)e FA(S)2125 1519 y Fj(\000)2184 1555 y Fu(.)100
1672 y(Consider)j(the)f(cell)g Fs(C)921 1687 y Fo(south)1128
1672 y Fu(de\014ned)h(b)m(y)f(colours)g(1)p Fs(;)17 b(:)g(:)g(:)f(;)h
(d)33 b Fu(of)g FA(S)2459 1636 y Fj(\000)2552 1672 y
Fu(on)g Fr(S)2743 1636 y Fq(d)2818 1672 y Fu(whic)m(h)i(con)m(tains)g
(the)f(South)0 1788 y(P)m(ole)49 b Fs(p)280 1803 y Fo(south)506
1788 y Fu(=)54 b(\(0)p Fs(;)17 b Fu(0)p Fs(;)g(:)g(:)g(:)e(;)i
Fu(0)p Fs(;)g Fn(\000)p Fu(1\).)88 b(W)-8 b(e)49 b(claim)f(this)h(is)f
(exactly)h(the)f(in)m(tersection)i(of)d Fr(S)3438 1752
y Fq(d)3527 1788 y Fu(with)i(the)0 1904 y(single)39 b(colourful)g
(simplicial)g(cone)g Fs(K)1437 1919 y Fo(Cap)1605 1904
y Fu(de\014ned)h(b)m(y)f(the)f Fs(d)g Fu(colourful)h(p)s(oin)m(ts)g(on)
f(Capricorn.)61 b(This)0 2020 y(follo)m(ws)32 b(since)g(an)m(y)g(other)
f(colourful)h(cone)f(is)h(generated)g(b)m(y)g(a)f(set)h(of)e
Fs(d)h Fu(coloured)h(p)s(oin)m(ts)f(c)m(hosen)i(from)0
2137 y(Capricorn,)h(Cancer)g(and)e(the)i(northern)f(p)s(olar)f(region.)
45 b(Fix)33 b(suc)m(h)h(a)f(cone)g(and)g(call)g(these)h(sets)g
Fs(G)3743 2152 y Fo(Cap)3873 2137 y Fu(,)0 2253 y Fs(G)77
2268 y Fo(Can)233 2253 y Fu(and)26 b Fs(G)493 2268 y
Fo(P)n(ole)655 2253 y Fu(and)h(let)f Fs(K)1056 2268 y
Fq(G)1143 2253 y Fu(=)i(cone\()p Fs(G)1551 2268 y Fo(Cap)1690
2253 y Fn([)9 b Fs(G)1842 2268 y Fo(Can)1981 2253 y Fn([)g
Fs(G)2133 2268 y Fo(P)n(ole)2270 2253 y Fu(\).)41 b(W)-8
b(e)27 b(assume)g(that)f(w)m(e)i(ha)m(v)m(e)f Fn(j)p
Fs(G)3534 2268 y Fo(Cap)3663 2253 y Fn(j)h Fs(<)f(d)p
Fu(.)0 2369 y(W)-8 b(e)31 b(need)h(to)f(sho)m(w)h(that)f(in)m(t\()p
Fs(K)1197 2384 y Fo(Cap)1327 2369 y Fu(\))18 b Fn(\\)i
Fu(in)m(t\()p Fs(K)1706 2384 y Fq(G)1765 2369 y Fu(\))28
b(=)f Fn(;)p Fu(.)43 b(T)-8 b(o)31 b(do)g(this,)h(w)m(e)g(\014nd)f(a)g
(h)m(yp)s(erplane)h(separating)0 2485 y Fs(K)83 2500
y Fo(Cap)242 2485 y Fu(and)d Fs(K)511 2500 y Fq(G)570
2485 y Fu(.)43 b(If)29 b Fs(G)811 2500 y Fo(Cap)968 2485
y Fu(=)f Fn(;)h Fu(the)g(h)m(yp)s(erplane)i(through)e(the)h(Equator)g
(will)g(do.)42 b(Otherwise,)31 b(tak)m(e)g(the)0 2602
y(colours)36 b(from)f Fs(G)644 2617 y Fo(Cap)808 2602
y Fu(and)h(consider)g(an)m(y)g(facet)f Fs(F)49 b Fu(of)35
b Fs(K)2117 2617 y Fo(Cap)2282 2602 y Fu(con)m(taining)h(generators)f
(of)g(eac)m(h)h(of)f(these)0 2718 y(colours.)42 b(Then)26
b Fs(F)40 b Fu(separates)26 b Fs(K)1216 2733 y Fo(Cap)1372
2718 y Fu(from)f(all)g(the)h(p)s(olar)f(p)s(oin)m(ts)h(and)g(all)g(the)
g(Cancer)g(p)s(oin)m(ts)g(of)f(colours)0 2834 y(from)36
b Fn(f)p Fu(1)p Fs(;)17 b Fu(2)p Fs(;)g(:)g(:)g(:)d(;)j(n)p
Fn(g)25 b(n)f Fs(G)927 2849 y Fo(Cap)1056 2834 y Fu(.)54
b(\(T)-8 b(o)35 b(b)s(e)i(absolutely)g(prop)s(er,)g(in)f(higher)g
(dimension)h(w)m(e)g(w)m(ould)g(ha)m(v)m(e)g(to)0 2950
y(mo)m(v)m(e)g(Capricorn)g(up)f(to)m(w)m(ards)h(the)f(equator)h(to)e
(ensure)j(the)e(separation)g(of)g(the)g(Cancer)h(p)s(oin)m(ts,)g(i.e.)0
3066 y(w)m(e)i(w)m(ould)g(ha)m(v)m(e)g(to)f(reduce)h(the)f(constan)m(t)
h(2)p Fs(\017)f Fu(to)g(\(1)25 b(+)h Fs(\016)t Fu(\))p
Fs(\017)38 b Fu(for)f(some)i Fs(\016)i(>)c Fu(0.\))59
b(This)39 b(completes)h(the)0 3183 y(pro)s(of.)h(W)-8
b(e)26 b(conclude)i(that)e(the)h(cell)g Fs(C)1451 3198
y Fo(south)1650 3183 y Fu(is)g(co)m(v)m(ered)i(only)d(b)m(y)i(the)f
(colourful)f(cone)h Fs(K)3281 3198 y Fo(Cap)3437 3183
y Fu(and)f(closely)0 3299 y(appro)m(ximates)34 b(the)f(spherical)h(cap)
f(b)s(ounded)g(b)m(y)h(Capricorn.)100 3415 y(It)k(is)h(a)g(go)s(o)s(d)e
(strategy)i(to)g(place)g(the)g(an)m(tip)s(o)s(des)g Fn(\000)p
Fs(p)2159 3430 y Fq(i)2226 3415 y Fu(in)g Fs(C)2416 3430
y Fo(south)2589 3415 y Fu(.)62 b(If)38 b(w)m(e)i(do)e(this)i(for)e(all)
g(of)g Fs(S)3748 3374 y Fj(\000)3742 3443 y Fq(d)p Fo(+1)3873
3415 y Fu(,)0 3539 y(ho)m(w)m(ev)m(er,)g(the)d(resulting)h
(con\014guration)f(will)g(not)g(ha)m(v)m(e)h FA(0)c Fn(2)g
Fu(con)m(v)r(\()p Fs(S)2646 3498 y Fj(\000)2640 3567
y Fq(d)p Fo(+1)2771 3539 y Fu(\))j(\()p Fs(S)2948 3498
y Fj(\000)2942 3567 y Fq(d)p Fo(+1)3107 3539 y Fu(w)m(ould)h(certainly)
g(b)s(e)0 3657 y(con)m(tained)i(in)f(an)g(op)s(en)g(hemisphere\).)59
b(So)36 b(w)m(e)i(m)m(ust)g(ha)m(v)m(e)g(at)f(least)g(one)g(an)m(tip)s
(o)s(de,)i(sa)m(y)e Fn(\000)p Fs(p)3579 3672 y Fo(1)3656
3657 y Fu(ab)s(o)m(v)m(e)0 3773 y(Capricorn.)52 b(Indeed,)38
b(if)d(w)m(e)h(place)g(the)g(remaining)f Fn(\000)p Fs(p)2093
3788 y Fq(i)2157 3773 y Fu(b)s(elo)m(w)h(Capricorn,)h(w)m(e)f(w)m(ould)
g(need)h(to)e(ha)m(v)m(e)0 3890 y Fn(\000)p Fs(p)126
3905 y Fo(1)203 3890 y Fu(ab)s(o)m(v)m(e)j(the)f(ring)g(of)g(the)g(an)m
(tip)s(o)s(des)h(of)e(Capricorn.)58 b(More)37 b(precisely)-8
b(,)40 b(this)e(is)g(the)f(set)h(of)e(p)s(oin)m(ts)0
4006 y(on)c Fr(S)190 3970 y Fq(d)264 4006 y Fu(with)h(\014nal)g(co)s
(ordinate)f(v)-5 b(alue)33 b(exactly)h(2)p Fs(\017)p
Fu(.)44 b(In)33 b(particular,)g(it)f(is)h(ab)s(o)m(v)m(e)h(Cancer.)100
4122 y(Let)k Fs(A)g Fu(=)f Fn(f)p Fs(a)605 4137 y Fo(1)644
4122 y Fs(;)17 b(a)739 4137 y Fo(2)779 4122 y Fs(;)g(:)g(:)g(:)f(;)h(a)
1049 4137 y Fq(d)1089 4122 y Fn(g)38 b Fu(b)s(e)h(the)f(p)s(oin)m(ts)h
(from)f Fs(S)2090 4081 y Fj(\000)2084 4146 y Fo(1)2149
4122 y Fs(;)17 b(S)2259 4081 y Fj(\000)2253 4146 y Fo(2)2318
4122 y Fs(;)g(:)g(:)g(:)e(;)i(S)2602 4081 y Fj(\000)2596
4150 y Fq(d)2699 4122 y Fu(on)38 b(Capricorn.)62 b(Similarly)-8
b(,)41 b(let)0 4238 y Fs(B)33 b Fu(=)27 b Fn(f)p Fs(b)301
4253 y Fo(1)341 4238 y Fs(;)17 b(b)426 4253 y Fo(2)466
4238 y Fs(;)g(:)g(:)g(:)e(;)i(b)725 4253 y Fq(d)766 4238
y Fn(g)27 b Fu(b)s(e)g(the)g(p)s(oin)m(ts)h(on)e(Cancer.)43
b(Let's)28 b(coun)m(t)f(ho)m(w)h(man)m(y)g(simplicial)g(cones)g(from)f
FA(S)3841 4202 y Fj(\000)0 4355 y Fu(m)m(ust)k(con)m(tain)f
Fn(\000)p Fs(p)706 4370 y Fo(1)775 4355 y Fu(if)g(w)m(e)h(place)f
Fn(\000)p Fs(p)1375 4370 y Fo(1)1444 4355 y Fu(ab)s(o)m(v)m(e)h
(Cancer.)43 b(T)-8 b(o)30 b(do)g(this,)g(w)m(e)h(start)f(with)g
Fn(\000)p Fs(p)3290 4370 y Fo(1)3359 4355 y Fu(in)g Fs(C)3540
4370 y Fo(south)3743 4355 y Fu(and)0 4471 y(then)25 b(mo)m(v)m(e)i(it)d
(ab)s(o)m(v)m(e)i(Cancer)g(noting)e(whic)m(h)j(cell)e(b)s(oundaries)h
(it)f(crosses)h(as)f(suggested)i(in)e(Section)g(3.2.)0
4587 y(This)40 b(structure)g(of)e(the)i(cell)f(b)s(oundaries)h(is)f(a)g
(top)s(ological)f(question,)k(so)d(w)m(e)h(\014nd)f(it)g(con)m(v)m
(enien)m(t)i(to)0 4703 y(remo)m(v)m(e)34 b(the)f Fs(p)550
4718 y Fo(south)756 4703 y Fu(and)g(equate)g Fr(S)1312
4667 y Fq(d)1386 4703 y Fu(with)g Fr(R)1680 4667 y Fq(d)p
Fj(\000)p Fo(1)1810 4703 y Fu(.)100 4819 y(With)25 b(the)g(exception)h
(of)e(the)h(single)h(colourful)e(cone)i(that)e(con)m(tains)i
Fs(C)2717 4834 y Fo(south)2889 4819 y Fu(,)h(the)e(colourful)f
(simplicial)0 4936 y(cones)41 b(generated)f(b)m(y)g FA(S)923
4900 y Fj(\000)1022 4936 y Fu(corresp)s(ond)g(to)f(colourful)h
(simplices)h(in)f Fr(R)2674 4900 y Fq(d)p Fj(\000)p Fo(1)2805
4936 y Fu(.)64 b(The)40 b(p)s(olar)f(p)s(oin)m(ts)h(on)f
Fr(S)3859 4900 y Fq(d)0 5052 y Fu(will)h(b)s(e)g(clustered)i(near)e
(the)g(origin)g(in)g Fr(R)1627 5016 y Fq(d)p Fj(\000)p
Fo(1)1758 5052 y Fu(.)65 b(Let)40 b Fs(A)2105 5016 y
Fj(0)2168 5052 y Fu(=)g Fn(f)p Fs(a)2385 5016 y Fj(0)2385
5077 y Fo(1)2424 5052 y Fs(;)17 b(:)g(:)g(:)f(;)h(a)2694
5016 y Fj(0)2694 5078 y Fq(d)2734 5052 y Fn(g)40 b Fu(and)g
Fs(B)3100 5016 y Fj(0)3163 5052 y Fu(=)g Fn(f)p Fs(b)3370
5016 y Fj(0)3370 5077 y Fo(1)3410 5052 y Fs(;)17 b(:)g(:)g(:)f(;)h(b)
3670 5016 y Fj(0)3670 5078 y Fq(d)3710 5052 y Fn(g)40
b Fu(b)s(e)0 5168 y(the)35 b(pro)5 b(jections)37 b(of)d
Fs(A)h Fu(and)g Fs(B)40 b Fu(resp)s(ectiv)m(ely)f(in)c
Fr(R)1925 5132 y Fq(d)p Fj(\000)p Fo(1)2055 5168 y Fu(.)51
b(Then)36 b(con)m(v)s(\()p Fs(A)2698 5132 y Fj(0)2721
5168 y Fu(\))f(and)g(con)m(v)r(\()p Fs(B)3299 5132 y
Fj(0)3323 5168 y Fu(\))g(form)f(nested)p eop end
%%Page: 9 9
TeXDict begin 9 8 bop 1304 71 a Fl(COLOURFUL)32 b(SIMPLICIAL)g(DEPTH)
1266 b(9)0 274 y Fu(simplices)37 b(whic)m(h)e(con)m(tain)g(the)f(pro)5
b(jection)35 b(of)f(the)h(p)s(olar)e(region.)48 b(The)36
b(b)s(oundaries)f(of)e(the)i(colourful)0 390 y(simplicial)e(cones)f(on)
f Fr(S)881 354 y Fq(d)952 390 y Fu(map)h(to)e(facets)i(of)e(simplices)k
(in)d Fr(R)2263 354 y Fq(d)p Fj(\000)p Fo(1)2394 390
y Fu(;)g(b)s(oth)g(are)g(de\014ned)i(b)m(y)e(sets)i(of)d(\()p
Fs(d)19 b Fn(\000)g Fu(1\))0 506 y(colourful)30 b(p)s(oin)m(ts.)43
b(Mo)m(ving)30 b Fn(\000)p Fs(p)1203 521 y Fo(1)1273
506 y Fu(from)f(b)s(elo)m(w)i(Capricorn)f(to)f(ab)s(o)m(v)m(e)h(Cancer)
h(corresp)s(onds)g(to)e(mo)m(ving)0 623 y Fn(\000)p Fs(p)126
586 y Fj(0)126 647 y Fo(1)198 623 y Fu(from)k(outside)g(con)m(v)s(\()p
Fs(A)1073 586 y Fj(0)1096 623 y Fu(\))g(to)f(inside)i(con)m(v)r(\()p
Fs(B)1876 586 y Fj(0)1900 623 y Fu(\).)100 739 y(Let)f(us)g(no)m(w)g
(see)h(what)f(simplicial)h(facets)g Fn(\000)p Fs(p)1840
703 y Fj(0)1840 763 y Fo(1)1912 739 y Fu(m)m(ust)g(cross)g(to)e(do)h
(this.)44 b(If)33 b(w)m(e)h(k)m(eep)g Fn(\000)p Fs(p)3467
703 y Fj(0)3467 763 y Fo(1)3539 739 y Fu(far)f(a)m(w)m(a)m(y)0
855 y(from)j(the)h Fs(a)457 819 y Fj(0)457 880 y Fq(i)521
855 y Fu(and)g Fs(b)756 819 y Fj(0)756 880 y Fq(i)784
855 y Fu('s)g(themselv)m(es,)k(w)m(e)c(can)f(a)m(v)m(oid)h(an)m(y)g
(facets)g(in)m(v)m(olving)h(the)f(p)s(olar)f(p)s(oin)m(ts:)51
b(These)0 971 y(facets)37 b(in)m(v)m(olv)m(e)h(at)d(most)i(\()p
Fs(d)24 b Fn(\000)g Fu(2\))36 b(generators)g(from)g Fs(A)2093
935 y Fj(0)2152 971 y Fu(and)g Fs(B)2424 935 y Fj(0)2448
971 y Fu(,)g(and)g(hence)i(ha)m(v)m(e)f(ends)g(that)e(are)h(at)0
1087 y(most)30 b(\()p Fs(d)16 b Fn(\000)g Fu(3\))30 b(dimensional)h
(manifolds)f(in)g(con)m(v)r(\()p Fs(A)1942 1051 y Fj(0)1966
1087 y Fu(\))16 b Fn(n)g Fu(in)m(t\(con)m(v)r(\()p Fs(B)2553
1051 y Fj(0)2577 1087 y Fu(\)\).)42 b(The)31 b(ends)f(can)g(b)s(e)g(a)m
(v)m(oided)h(b)m(y)0 1204 y(Lemma)i(3.3.)100 1320 y(This)39
b(still)g(lea)m(v)m(es)h Fs(d)p Fu(2)909 1284 y Fq(d)p
Fj(\000)p Fo(1)1077 1320 y Fu(colourful)f(facets)g(de\014ned)g(b)m(y)g
(c)m(ho)s(osing)g(\()p Fs(d)26 b Fn(\000)g Fu(1\))38
b(colourful)g(p)s(oin)m(ts)h(from)0 1436 y Fs(A)73 1400
y Fj(0)135 1436 y Fu(and)g Fs(B)410 1400 y Fj(0)434 1436
y Fu(.)62 b(W)-8 b(e)39 b(can)g(en)m(umerate)h(them)g(b)m(y)g(\014rst)f
(c)m(ho)s(osing)g(an)g(index)h(\(colour\))f(to)g(omit)f(and)h(then)0
1552 y(represen)m(ting)32 b(the)e(c)m(hoices)i(of)d Fs(a)1198
1516 y Fj(0)1198 1577 y Fq(i)1226 1552 y Fu('s)i(and)f
Fs(b)1550 1516 y Fj(0)1550 1577 y Fq(i)1578 1552 y Fu('s)h(b)m(y)f(a)g
(0-1)f(v)m(ector)i(of)e(length)h(\()p Fs(d)16 b Fn(\000)g
Fu(1\).)43 b(Letting)30 b(0)g(represen)m(t)0 1669 y(the)e(c)m(hoice)g
(of)f(an)g Fs(a)734 1632 y Fj(0)734 1693 y Fq(i)762 1669
y Fu(,)i(con)m(v)r(\()p Fs(A)1125 1632 y Fj(0)1148 1669
y Fu(\))f(is)f(b)s(ounded)h(b)m(y)g(the)g(facets)g(de\014ned)g(b)m(y)g
Fs(d)f Fu(index)i(c)m(hoices)g(and)e(a)g(v)m(ector)0
1785 y(of)37 b(0's,)j(while)f(con)m(v)r(\()p Fs(B)870
1749 y Fj(0)894 1785 y Fu(\))e(is)i(b)s(ounded)f(b)m(y)h(the)f(facets)h
(de\014ned)g(b)m(y)g Fs(d)e Fu(index)i(c)m(hoices)h(and)e(a)g(v)m
(ector)g(of)0 1901 y(1's.)k(In)28 b(fact)f(there)h(are)g(2)938
1865 y Fq(d)1005 1901 y Fu(colourful)g(simplices)i(generated)e(b)m(y)g
Fs(A)2454 1865 y Fj(0)2505 1901 y Fu(and)g Fs(B)2769
1865 y Fj(0)2792 1901 y Fu(,)h(and)e(they)i(are)e(en)m(umerated)0
2017 y(b)m(y)35 b(0-1)f(v)m(ectors)i(of)e(length)h Fs(d)p
Fu(.)49 b(Their)36 b(facets)f(are)f(en)m(umerated)j(b)m(y)e(c)m(ho)s
(osing)g(an)g(index)g(to)g(drop)f(from)0 2134 y(the)g(en)m(umerating)i
(sequence.)50 b(Therefore)35 b(the)f(sums)h(of)f(the)g(0-1)f(v)m
(ectors)i(en)m(umerating)h(the)e(facets)g(of)0 2250 y(a)e(giv)m(en)i
(simplex)h(can)d(di\013er)h(b)m(y)h(at)e(most)h(1.)100
2366 y(No)m(w)40 b(start)g(with)g Fn(\000)p Fs(p)925
2330 y Fj(0)925 2391 y Fo(1)1005 2366 y Fu(outside)h(con)m(v)r(\()p
Fs(A)1656 2330 y Fj(0)1680 2366 y Fu(\).)65 b(T)-8 b(o)40
b(bring)g Fn(\000)p Fs(p)2349 2330 y Fj(0)2349 2391 y
Fo(1)2429 2366 y Fu(inside)h(con)m(v)r(\()p Fs(B)3026
2330 y Fj(0)3050 2366 y Fu(\),)g(w)m(e)g(m)m(ust)g(start)f(b)m(y)0
2482 y(bringing)f(it)g(in)m(to)g(con)m(v)s(\()p Fs(A)1007
2446 y Fj(0)1030 2482 y Fu(\).)63 b(This)40 b(in)m(v)m(olv)m(es)h
(crossing)f(some)g(b)s(oundary)g(face)f(of)f(con)m(v)s(\()p
Fs(A)3461 2446 y Fj(0)3484 2482 y Fu(\),)j(sa)m(y)f(the)0
2598 y(one)27 b(de\014ned)h(b)m(y)f Fs(a)683 2613 y Fo(1)722
2598 y Fs(;)17 b(:)g(:)g(:)f(;)h(a)992 2613 y Fq(d)p
Fj(\000)p Fo(1)1123 2598 y Fu(.)41 b(This)28 b(is)f(en)m(umerated)h(as)
f(\()p Fs(d;)17 b Fu(0)p Fs(;)g Fu(0)p Fs(;)g(:)g(:)g(:)d(;)j
Fu(0)p Fs(;)g Fu(0\).)40 b(W)-8 b(e)27 b(can)g(pro)s(ceed)g(through)0
2715 y(facets)33 b(\()p Fs(d)21 b Fn(\000)g Fu(1)p Fs(;)c
Fu(0)p Fs(;)g Fu(0)p Fs(;)g(:)g(:)g(:)e(;)i Fu(0)p Fs(;)g
Fu(1\),)31 b(\()p Fs(d)21 b Fn(\000)h Fu(2)p Fs(;)17
b Fu(0)p Fs(;)g Fu(0)p Fs(;)g(:)g(:)g(:)d(;)j Fu(0)p
Fs(;)g Fu(1)p Fs(;)g Fu(1\))31 b(un)m(til)i(\014nally)g(w)m(e)g(cross)g
(\(1)p Fs(;)17 b Fu(1)p Fs(;)g Fu(1)p Fs(;)g(:)g(:)g(:)d(;)j
Fu(1\))32 b(in)m(to)g(a)0 2831 y(cell)i(of)f(con)m(v)r(\()p
Fs(B)599 2795 y Fj(0)623 2831 y Fu(\).)45 b(This)35 b(in)m(v)m(olv)m
(es)h Fs(d)d Fu(facet)g(crossings,)i(whic)m(h)g(is)f(minimal)g(since)g
(at)f(eac)m(h)i(crossing)f(w)m(e)0 2947 y(can)f(only)g(add)g(a)f
(single)h(1)g(to)f(the)h(0-1)e(part)i(of)f(the)h(en)m(umerating)h(v)m
(ector.)100 3063 y(W)-8 b(e)30 b(claim)g(that)f(as)h
Fn(\000)p Fs(p)973 3027 y Fj(0)973 3088 y Fo(1)1042 3063
y Fu(crosses)i(eac)m(h)e(facet,)h(it)e(mak)m(es)j(a)d(net)h(gain)f(of)h
Fs(d)16 b Fn(\000)g Fu(1)29 b(con)m(taining)h(simplices.)0
3180 y(A)m(t)44 b(the)h(\014rst)g(facet,)i(\()p Fs(d;)17
b Fu(0)p Fs(;)g Fu(0)p Fs(;)g(:)g(:)g(:)d(;)j Fu(0)p
Fs(;)g Fu(0\),)46 b Fn(\000)p Fs(p)1693 3143 y Fj(0)1693
3204 y Fo(1)1777 3180 y Fu(lea)m(v)m(es)g(the)f(single)g(exterior)g
(simplex)h(de\014ned)f(b)m(y)h(the)0 3296 y(p)s(oin)m(ts)39
b Fs(A)372 3260 y Fj(0)433 3296 y Fu(pro)5 b(jected)39
b(from)f(Capricorn)h(and)f(en)m(ters)h(the)g Fs(d)e Fu(simplices)k
(de\014ned)e(b)m(y)g Fs(a)3265 3260 y Fj(0)3265 3320
y Fo(1)3305 3296 y Fs(;)17 b(:)g(:)g(:)e(;)i(a)3574 3260
y Fj(0)3574 3322 y Fq(d)p Fj(\000)p Fo(1)3743 3296 y
Fu(and)0 3412 y(the)26 b Fs(d)f Fu(p)s(oin)m(ts)i(of)e(colour)h
Fs(d)f Fu(other)h(than)f Fs(a)1509 3376 y Fj(0)1509 3438
y Fq(d)1550 3412 y Fu(.)41 b(A)m(t)26 b(subsequen)m(t)j(facet)d
(crossings,)i(the)f(same)f(thing)g(happ)s(ens)0 3528
y(for)35 b(the)i(remaining)f(colours:)51 b Fn(\000)p
Fs(p)1284 3492 y Fj(0)1284 3553 y Fo(1)1360 3528 y Fu(lea)m(v)m(es)38
b(the)f(simplex)g(de\014ned)h(b)m(y)f(the)f(crossing)h(facet)f(and)g
Fs(a)3679 3492 y Fj(0)3679 3553 y Fq(i)3708 3528 y Fu(.)53
b(As)0 3645 y Fn(\000)p Fs(p)126 3608 y Fj(0)126 3669
y Fo(1)197 3645 y Fu(lea)m(v)m(es,)33 b(it)e(en)m(ters)h(the)g
(simplices)h(de\014ned)f(b)m(y)g(this)g(facet)f(and)g(the)g
Fs(d)f Fu(remaining)i(p)s(oin)m(ts)f(of)g(colour)0 3761
y Fs(i)p Fu(.)56 b(Hence)38 b(the)g(n)m(um)m(b)s(er)g(of)e(simplices)j
(con)m(taining)f Fn(\000)p Fs(p)2079 3725 y Fj(0)2079
3785 y Fo(1)2155 3761 y Fu(immediately)h(after)d(crossing)i(in)m(to)f
(con)m(v)s(\()p Fs(B)3839 3725 y Fj(0)3862 3761 y Fu(\))0
3877 y(is)c(exactly)h(1)22 b(+)g Fs(d)p Fu(\()p Fs(d)f
Fn(\000)i Fu(1\).)100 3993 y(W)-8 b(e)44 b(will)g(no)m(w)g(return)g
(our)f(atten)m(tion)h(to)g Fr(S)1798 3957 y Fq(d)1838
3993 y Fu(.)77 b(Denote)43 b(b)m(y)i Fs(C)2504 4008 y
Fq(p)2587 3993 y Fu(the)f(cell)g(con)m(taining)g Fn(\000)p
Fs(p)3561 4008 y Fo(1)3645 3993 y Fu(whose)0 4109 y(pro)5
b(jection)34 b(lies)h(inside)g(con)m(v)r(\()p Fs(B)1225
4073 y Fj(0)1248 4109 y Fu(\).)47 b(F)-8 b(rom)33 b(our)g
(construction,)i Fs(C)2448 4124 y Fq(p)2521 4109 y Fu(is)f(a)f(cell)i
(ab)s(o)m(v)m(e)f(Cancer.)47 b(W)-8 b(e)34 b(w)m(an)m(t)0
4226 y(to)26 b(claim)h(that)g(in)g(fact)f(it)h(con)m(tains)g(some)h(p)s
(oin)m(t)f(ab)s(o)m(v)m(e)g(the)g(set)g(of)f(an)m(tip)s(o)s(des)i(of)e
(Capricorn,)i(that)f(is,)h(a)0 4342 y(p)s(oin)m(t)j(whose)h(an)m(tip)s
(o)s(de)e(is)i(in)e Fs(C)1218 4357 y Fo(south)1391 4342
y Fu(.)43 b(This)32 b(is)f(a)g(complicated)h(geometric)f(calculation.)
43 b(Ho)m(w)m(ev)m(er,)34 b(w)m(e)0 4458 y(observ)m(e)k(that)d(nothing)
h(in)g(our)g(top)s(ological)f(argumen)m(t)i(ab)s(o)m(v)m(e)f(c)m
(hanges)i(if)d(w)m(e)i(c)m(hange)g(the)f(constan)m(t)0
4574 y(2)p Fs(\017)k Fu(in)g(our)f(de\014nition)i(of)e(Capricorn)i(to)e
Fs(c)27 b(\017)40 b Fu(for)f(an)m(y)i Fs(c)e Fn(\025)i
Fu(0.)64 b(In)40 b(particular,)i(the)e(cell)h Fs(C)3453
4589 y Fq(p)3532 4574 y Fu(do)s(es)f(not)0 4691 y(degenerate)47
b(if)e(w)m(e)h(mo)m(v)m(e)h(the)f(an)m(tip)s(o)s(des)g(of)f(Capricorn)h
(to)m(w)m(ards)g(Cancer)h(b)m(y)f(decreasing)h Fs(c)e
Fu(to)g(1.)0 4807 y(Therefore)37 b(for)e(some)i Fs(c)c(>)h
Fu(1)h(\(this)i(condition)f(main)m(tains)h FA(0)d Fn(2)f
Fu(in)m(t)q(\(con)m(v)r(\()p Fs(S)2872 4766 y Fj(\000)2866
4832 y Fq(i)2931 4807 y Fu(\)\))j(for)f Fs(i)f Fu(=)f(1)p
Fs(;)17 b(:)g(:)g(:)e(;)i(d)p Fu(\),)37 b Fs(C)3861 4822
y Fq(p)0 4923 y Fu(includes)31 b(some)f(p)s(oin)m(t)f(ab)s(o)m(v)m(e)h
(the)g(an)m(tip)s(o)s(des)g(of)e(Capricorn.)43 b(An)m(y)31
b(suc)m(h)f Fs(c)f Fu(and)g(p)s(oin)m(t)h(in)f Fs(C)3450
4938 y Fq(p)3519 4923 y Fu(w)m(ould)h(b)s(e)0 5039 y(su\016cien)m(t)j
(for)d(our)h(construction.)44 b(W)-8 b(e)31 b(ha)m(v)m(e)h(used)g
Fs(c)27 b Fu(=)h(2)i(for)g(concreteness)k(and)d(tak)m(e)g(it)g(as)g(an)
f(article)0 5156 y(of)i(faith)g(that)h(this)g(is)g(a)f(small)i(enough)f
(for)f(our)g(c)m(hoice)i(of)e Fs(\017)p Fu(.)p eop end
%%Page: 10 10
TeXDict begin 10 9 bop 0 75 a Fl(10)498 b(ANTOINE)25
b(DEZA,)g(SUI)f(HUANG,)h(T)-6 b(AMON)25 b(STEPHEN)h(AND)e(T)-6
b(AM)2823 56 y(\023)2813 75 y(AS)25 b(TERLAKY)1321 1487
y @beginspecial 0 @llx 0 @lly 271 @urx 275 @ury 1530
@rhi @setspecial
%%BeginDocument: placement.eps
%!PS-Adobe-2.0 EPSF-2.0
%%Title: placement.eps
%%Creator: fig2dev Version 3.2 Patchlevel 3c
%%CreationDate: Fri May 27 15:25:00 2005
%%For: tamon@birkhoff (Tamon Stephen,TTCA)
%%BoundingBox: 0 0 271 275
%%Magnification: 1.0000
%%EndComments
/$F2psDict 200 dict def
$F2psDict begin
$F2psDict /mtrx matrix put
/col-1 {0 setgray} bind def
/col0 {0.000 0.000 0.000 srgb} bind def
/col1 {0.000 0.000 1.000 srgb} bind def
/col2 {0.000 1.000 0.000 srgb} bind def
/col3 {0.000 1.000 1.000 srgb} bind def
/col4 {1.000 0.000 0.000 srgb} bind def
/col5 {1.000 0.000 1.000 srgb} bind def
/col6 {1.000 1.000 0.000 srgb} bind def
/col7 {1.000 1.000 1.000 srgb} bind def
/col8 {0.000 0.000 0.560 srgb} bind def
/col9 {0.000 0.000 0.690 srgb} bind def
/col10 {0.000 0.000 0.820 srgb} bind def
/col11 {0.530 0.810 1.000 srgb} bind def
/col12 {0.000 0.560 0.000 srgb} bind def
/col13 {0.000 0.690 0.000 srgb} bind def
/col14 {0.000 0.820 0.000 srgb} bind def
/col15 {0.000 0.560 0.560 srgb} bind def
/col16 {0.000 0.690 0.690 srgb} bind def
/col17 {0.000 0.820 0.820 srgb} bind def
/col18 {0.560 0.000 0.000 srgb} bind def
/col19 {0.690 0.000 0.000 srgb} bind def
/col20 {0.820 0.000 0.000 srgb} bind def
/col21 {0.560 0.000 0.560 srgb} bind def
/col22 {0.690 0.000 0.690 srgb} bind def
/col23 {0.820 0.000 0.820 srgb} bind def
/col24 {0.500 0.190 0.000 srgb} bind def
/col25 {0.630 0.250 0.000 srgb} bind def
/col26 {0.750 0.380 0.000 srgb} bind def
/col27 {1.000 0.500 0.500 srgb} bind def
/col28 {1.000 0.630 0.630 srgb} bind def
/col29 {1.000 0.750 0.750 srgb} bind def
/col30 {1.000 0.880 0.880 srgb} bind def
/col31 {1.000 0.840 0.000 srgb} bind def
/col32 {0.255 0.255 0.255 srgb} bind def
/col33 {0.525 0.510 0.525 srgb} bind def
/col34 {0.745 0.765 0.745 srgb} bind def
/col35 {0.875 0.890 0.875 srgb} bind def
/col36 {0.525 0.510 0.525 srgb} bind def
/col37 {0.745 0.765 0.745 srgb} bind def
/col38 {0.875 0.890 0.875 srgb} bind def
/col39 {0.286 0.271 0.286 srgb} bind def
/col40 {0.286 0.271 0.286 srgb} bind def
/col41 {0.557 0.557 0.557 srgb} bind def
/col42 {0.620 0.000 0.000 srgb} bind def
/col43 {0.620 0.000 0.000 srgb} bind def
/col44 {0.557 0.557 0.557 srgb} bind def
/col45 {0.255 0.255 0.255 srgb} bind def
/col46 {0.557 0.557 0.557 srgb} bind def
/col47 {0.255 0.255 0.255 srgb} bind def
/col48 {0.557 0.557 0.557 srgb} bind def
/col49 {0.255 0.255 0.255 srgb} bind def
/col50 {0.557 0.557 0.557 srgb} bind def
/col51 {0.255 0.255 0.255 srgb} bind def
/col52 {0.557 0.557 0.557 srgb} bind def
/col53 {0.255 0.255 0.255 srgb} bind def
/col54 {0.557 0.557 0.557 srgb} bind def
/col55 {0.255 0.255 0.255 srgb} bind def
/col56 {0.557 0.557 0.557 srgb} bind def
/col57 {0.255 0.255 0.255 srgb} bind def
/col58 {0.557 0.557 0.557 srgb} bind def
/col59 {0.255 0.255 0.255 srgb} bind def
/col60 {0.557 0.557 0.557 srgb} bind def
/col61 {0.255 0.255 0.255 srgb} bind def
/col62 {0.557 0.557 0.557 srgb} bind def
/col63 {0.255 0.255 0.255 srgb} bind def
/col64 {0.557 0.557 0.557 srgb} bind def
/col65 {0.255 0.255 0.255 srgb} bind def
/col66 {0.557 0.557 0.557 srgb} bind def
/col67 {0.255 0.255 0.255 srgb} bind def
/col68 {0.557 0.557 0.557 srgb} bind def
/col69 {0.255 0.255 0.255 srgb} bind def
/col70 {0.557 0.557 0.557 srgb} bind def
/col71 {0.255 0.255 0.255 srgb} bind def
/col72 {0.557 0.557 0.557 srgb} bind def
/col73 {0.255 0.255 0.255 srgb} bind def
/col74 {0.557 0.557 0.557 srgb} bind def
/col75 {0.255 0.255 0.255 srgb} bind def
/col76 {0.557 0.557 0.557 srgb} bind def
/col77 {0.255 0.255 0.255 srgb} bind def
/col78 {0.557 0.557 0.557 srgb} bind def
/col79 {0.255 0.255 0.255 srgb} bind def
/col80 {0.745 0.765 0.745 srgb} bind def
/col81 {0.412 0.427 0.412 srgb} bind def
/col82 {0.745 0.765 0.745 srgb} bind def
/col83 {0.412 0.427 0.412 srgb} bind def
/col84 {0.286 0.271 0.286 srgb} bind def
/col85 {0.557 0.557 0.557 srgb} bind def
/col86 {0.412 0.427 0.412 srgb} bind def
/col87 {0.557 0.557 0.557 srgb} bind def
/col88 {0.443 0.443 0.443 srgb} bind def
/col89 {0.682 0.682 0.682 srgb} bind def
/col90 {0.188 0.188 0.188 srgb} bind def
/col91 {0.588 0.573 0.588 srgb} bind def
/col92 {0.443 0.443 0.443 srgb} bind def
/col93 {0.349 0.333 0.349 srgb} bind def
/col94 {0.682 0.698 0.682 srgb} bind def
/col95 {0.745 0.765 0.745 srgb} bind def
/col96 {0.286 0.271 0.286 srgb} bind def
/col97 {0.412 0.427 0.412 srgb} bind def
/col98 {0.286 0.271 0.286 srgb} bind def
/col99 {0.412 0.427 0.412 srgb} bind def
/col100 {0.745 0.765 0.745 srgb} bind def
/col101 {0.412 0.427 0.412 srgb} bind def
/col102 {0.286 0.271 0.286 srgb} bind def
/col103 {0.745 0.765 0.745 srgb} bind def
/col104 {0.412 0.427 0.412 srgb} bind def
/col105 {0.745 0.765 0.745 srgb} bind def
/col106 {0.286 0.271 0.286 srgb} bind def
/col107 {0.557 0.557 0.557 srgb} bind def
/col108 {0.875 0.890 0.937 srgb} bind def
/col109 {0.588 0.588 0.620 srgb} bind def
/col110 {0.843 0.859 0.843 srgb} bind def
/col111 {0.620 0.635 0.714 srgb} bind def
/col112 {0.620 0.000 0.000 srgb} bind def
/col113 {0.937 0.937 0.937 srgb} bind def
/col114 {0.875 0.890 0.875 srgb} bind def
/col115 {0.525 0.682 1.000 srgb} bind def
/col116 {0.443 0.443 1.000 srgb} bind def
/col117 {0.875 0.620 0.557 srgb} bind def
/col118 {0.937 0.937 0.875 srgb} bind def
/col119 {0.875 0.796 0.682 srgb} bind def
/col120 {0.812 0.827 0.812 srgb} bind def
/col121 {0.843 0.475 0.094 srgb} bind def
/col122 {0.937 0.906 0.094 srgb} bind def
/col123 {0.557 0.490 0.745 srgb} bind def
/col124 {0.843 0.843 0.843 srgb} bind def
/col125 {0.557 0.557 0.651 srgb} bind def
/col126 {0.286 0.286 0.286 srgb} bind def
/col127 {0.557 0.412 0.412 srgb} bind def
/col128 {0.349 0.349 0.349 srgb} bind def
/col129 {0.380 0.380 0.380 srgb} bind def
/col130 {0.714 0.604 0.443 srgb} bind def
/col131 {0.255 0.573 1.000 srgb} bind def
/col132 {0.745 0.443 0.220 srgb} bind def
/col133 {0.843 0.459 0.000 srgb} bind def
/col134 {0.843 0.729 0.000 srgb} bind def
/col135 {0.000 0.396 0.000 srgb} bind def
/col136 {0.349 0.412 0.220 srgb} bind def
/col137 {0.812 0.827 0.812 srgb} bind def
/col138 {0.682 0.667 0.682 srgb} bind def
/col139 {0.557 0.557 0.651 srgb} bind def
/col140 {0.937 0.729 0.349 srgb} bind def
/col141 {0.557 0.604 0.412 srgb} bind def
/col142 {0.286 0.286 0.286 srgb} bind def
/col143 {0.380 0.396 0.380 srgb} bind def
/col144 {0.843 0.843 0.843 srgb} bind def
/col145 {0.557 0.557 0.651 srgb} bind def
/col146 {0.349 0.349 0.349 srgb} bind def
/col147 {0.380 0.380 0.380 srgb} bind def
/col148 {0.714 0.906 1.000 srgb} bind def
/col149 {0.525 0.765 0.937 srgb} bind def
/col150 {0.745 0.745 0.745 srgb} bind def
/col151 {0.812 0.588 0.318 srgb} bind def
/col152 {0.620 0.827 1.000 srgb} bind def
/col153 {0.843 0.843 0.843 srgb} bind def
/col154 {0.557 0.557 0.651 srgb} bind def
/col155 {0.557 0.412 0.412 srgb} bind def
/col156 {0.349 0.349 0.349 srgb} bind def
/col157 {0.380 0.380 0.380 srgb} bind def
/col158 {0.557 0.620 0.412 srgb} bind def
/col159 {0.969 0.412 0.000 srgb} bind def
/col160 {0.349 0.412 0.220 srgb} bind def
/col161 {0.557 0.620 0.412 srgb} bind def
/col162 {0.286 0.286 0.286 srgb} bind def
/col163 {0.843 0.843 0.843 srgb} bind def
/col164 {0.557 0.557 0.651 srgb} bind def
/col165 {0.557 0.412 0.412 srgb} bind def
/col166 {0.349 0.349 0.349 srgb} bind def
/col167 {0.380 0.380 0.380 srgb} bind def
/col168 {0.557 0.620 0.412 srgb} bind def
/col169 {0.969 0.412 0.000 srgb} bind def
/col170 {0.557 0.620 0.475 srgb} bind def
/col171 {0.286 0.286 0.286 srgb} bind def
/col172 {0.094 0.286 0.094 srgb} bind def
/col173 {0.349 0.412 0.220 srgb} bind def
/col174 {0.843 0.843 0.843 srgb} bind def
/col175 {0.557 0.557 0.651 srgb} bind def
/col176 {0.969 0.745 0.349 srgb} bind def
/col177 {0.557 0.620 0.412 srgb} bind def
/col178 {0.286 0.286 0.286 srgb} bind def
/col179 {0.380 0.380 0.380 srgb} bind def
/col180 {0.380 0.412 0.620 srgb} bind def
/col181 {0.557 0.412 0.412 srgb} bind def
/col182 {0.969 0.969 0.969 srgb} bind def
/col183 {0.875 0.000 0.000 srgb} bind def
/col184 {0.349 0.349 0.349 srgb} bind def
/col185 {0.557 0.620 0.412 srgb} bind def
/col186 {0.286 0.286 0.286 srgb} bind def
/col187 {0.380 0.380 0.380 srgb} bind def
/col188 {0.349 0.412 0.220 srgb} bind def
/col189 {0.843 0.843 0.843 srgb} bind def
/col190 {0.557 0.557 0.651 srgb} bind def
/col191 {0.969 0.745 0.349 srgb} bind def
/col192 {0.557 0.620 0.412 srgb} bind def
/col193 {0.286 0.286 0.286 srgb} bind def
/col194 {0.380 0.380 0.380 srgb} bind def
/col195 {0.349 0.412 0.220 srgb} bind def
/col196 {0.843 0.843 0.843 srgb} bind def
/col197 {0.557 0.557 0.651 srgb} bind def
/col198 {0.969 0.745 0.349 srgb} bind def
/col199 {0.557 0.620 0.412 srgb} bind def
/col200 {0.286 0.286 0.286 srgb} bind def
/col201 {0.380 0.380 0.380 srgb} bind def
/col202 {0.380 0.412 0.620 srgb} bind def
/col203 {0.318 0.412 0.157 srgb} bind def
/col204 {0.380 0.380 0.380 srgb} bind def
/col205 {0.349 0.412 0.220 srgb} bind def
/col206 {0.588 0.588 0.588 srgb} bind def
/col207 {0.380 0.380 0.380 srgb} bind def
/col208 {0.000 0.380 0.000 srgb} bind def
/col209 {0.557 0.557 0.651 srgb} bind def
/col210 {0.557 0.557 0.651 srgb} bind def
/col211 {0.557 0.557 0.651 srgb} bind def
/col212 {0.000 0.380 0.286 srgb} bind def
/col213 {0.475 0.525 0.286 srgb} bind def
/col214 {0.906 0.745 0.475 srgb} bind def
/col215 {0.557 0.620 0.475 srgb} bind def
/col216 {0.651 0.714 0.780 srgb} bind def
/col217 {0.412 0.412 0.588 srgb} bind def
/col218 {0.525 0.412 0.412 srgb} bind def
/col219 {0.318 0.620 0.286 srgb} bind def
/col220 {0.843 0.906 0.906 srgb} bind def
/col221 {0.318 0.380 0.380 srgb} bind def
/col222 {0.094 0.412 0.286 srgb} bind def
/col223 {0.620 0.651 0.714 srgb} bind def
/col224 {1.000 0.588 0.000 srgb} bind def
/col225 {1.000 0.588 0.000 srgb} bind def
/col226 {0.557 0.412 0.412 srgb} bind def
/col227 {0.000 0.380 0.286 srgb} bind def
/col228 {0.475 0.525 0.286 srgb} bind def
/col229 {0.380 0.443 0.475 srgb} bind def
/col230 {0.906 0.745 0.475 srgb} bind def
/col231 {0.094 0.286 0.094 srgb} bind def
/col232 {0.349 0.412 0.220 srgb} bind def
/col233 {0.557 0.557 0.651 srgb} bind def
/col234 {0.969 0.745 0.349 srgb} bind def
/col235 {0.557 0.620 0.412 srgb} bind def
/col236 {0.286 0.286 0.286 srgb} bind def
/col237 {0.380 0.380 0.380 srgb} bind def
/col238 {0.843 0.843 0.843 srgb} bind def
/col239 {0.557 0.557 0.651 srgb} bind def
/col240 {0.286 0.286 0.286 srgb} bind def
/col241 {0.380 0.380 0.380 srgb} bind def
/col242 {0.557 0.412 0.412 srgb} bind def
/col243 {0.349 0.349 0.349 srgb} bind def
/col244 {0.286 0.286 0.286 srgb} bind def
/col245 {0.380 0.380 0.380 srgb} bind def
/col246 {0.380 0.380 0.380 srgb} bind def
/col247 {0.557 0.620 0.412 srgb} bind def
/col248 {0.286 0.286 0.286 srgb} bind def
/col249 {0.349 0.412 0.220 srgb} bind def
/col250 {0.286 0.286 0.286 srgb} bind def
/col251 {0.000 0.396 0.000 srgb} bind def
/col252 {0.349 0.412 0.220 srgb} bind def
/col253 {0.812 0.827 0.812 srgb} bind def
/col254 {0.682 0.667 0.682 srgb} bind def
/col255 {0.557 0.557 0.651 srgb} bind def
/col256 {0.937 0.729 0.349 srgb} bind def
/col257 {0.557 0.604 0.412 srgb} bind def
/col258 {0.286 0.286 0.286 srgb} bind def
/col259 {0.380 0.396 0.380 srgb} bind def
/col260 {0.843 0.843 0.843 srgb} bind def
/col261 {0.557 0.557 0.651 srgb} bind def
/col262 {0.349 0.349 0.349 srgb} bind def
/col263 {0.380 0.380 0.380 srgb} bind def
/col264 {0.843 0.843 0.843 srgb} bind def
/col265 {0.349 0.412 0.220 srgb} bind def
/col266 {0.557 0.557 0.651 srgb} bind def
/col267 {0.557 0.412 0.412 srgb} bind def
/col268 {0.349 0.349 0.349 srgb} bind def
/col269 {0.380 0.380 0.380 srgb} bind def
/col270 {0.557 0.620 0.412 srgb} bind def
/col271 {0.286 0.286 0.286 srgb} bind def
/col272 {0.843 0.843 0.843 srgb} bind def
/col273 {0.557 0.557 0.651 srgb} bind def
/col274 {0.557 0.412 0.412 srgb} bind def
/col275 {0.349 0.349 0.349 srgb} bind def
/col276 {0.380 0.380 0.380 srgb} bind def
/col277 {0.557 0.620 0.475 srgb} bind def
/col278 {0.286 0.286 0.286 srgb} bind def
/col279 {0.000 0.380 0.000 srgb} bind def
/col280 {0.349 0.412 0.220 srgb} bind def
/col281 {0.875 0.875 0.875 srgb} bind def
/col282 {0.557 0.557 0.651 srgb} bind def
/col283 {0.969 0.745 0.349 srgb} bind def
/col284 {0.557 0.620 0.412 srgb} bind def
/col285 {0.286 0.286 0.286 srgb} bind def
/col286 {0.380 0.380 0.380 srgb} bind def
/col287 {0.380 0.412 0.620 srgb} bind def
/col288 {0.843 0.843 0.843 srgb} bind def
/col289 {0.557 0.412 0.412 srgb} bind def
/col290 {0.349 0.349 0.349 srgb} bind def
/col291 {0.000 0.396 0.000 srgb} bind def
/col292 {0.349 0.412 0.220 srgb} bind def
/col293 {0.812 0.827 0.812 srgb} bind def
/col294 {0.682 0.667 0.682 srgb} bind def
/col295 {0.557 0.557 0.651 srgb} bind def
/col296 {0.937 0.729 0.349 srgb} bind def
/col297 {0.557 0.604 0.412 srgb} bind def
/col298 {0.286 0.286 0.286 srgb} bind def
/col299 {0.380 0.396 0.380 srgb} bind def
/col300 {0.349 0.412 0.220 srgb} bind def
/col301 {0.812 0.827 0.812 srgb} bind def
/col302 {0.682 0.667 0.682 srgb} bind def
/col303 {0.557 0.557 0.651 srgb} bind def
/col304 {0.937 0.729 0.349 srgb} bind def
/col305 {0.557 0.604 0.412 srgb} bind def
/col306 {0.286 0.286 0.286 srgb} bind def
/col307 {0.380 0.396 0.380 srgb} bind def
/col308 {0.349 0.412 0.220 srgb} bind def
/col309 {0.812 0.827 0.812 srgb} bind def
/col310 {0.682 0.667 0.682 srgb} bind def
/col311 {0.557 0.557 0.651 srgb} bind def
/col312 {0.937 0.729 0.349 srgb} bind def
/col313 {0.557 0.604 0.412 srgb} bind def
/col314 {0.286 0.286 0.286 srgb} bind def
/col315 {0.380 0.396 0.380 srgb} bind def
/col316 {0.349 0.412 0.220 srgb} bind def
/col317 {0.812 0.827 0.812 srgb} bind def
/col318 {0.682 0.667 0.682 srgb} bind def
/col319 {0.557 0.557 0.651 srgb} bind def
/col320 {0.937 0.729 0.349 srgb} bind def
/col321 {0.557 0.604 0.412 srgb} bind def
/col322 {0.286 0.286 0.286 srgb} bind def
/col323 {0.380 0.396 0.380 srgb} bind def
/col324 {0.349 0.412 0.220 srgb} bind def
/col325 {0.812 0.827 0.812 srgb} bind def
/col326 {0.682 0.667 0.682 srgb} bind def
/col327 {0.557 0.557 0.651 srgb} bind def
/col328 {0.937 0.729 0.349 srgb} bind def
/col329 {0.557 0.604 0.412 srgb} bind def
/col330 {0.286 0.286 0.286 srgb} bind def
/col331 {0.380 0.396 0.380 srgb} bind def
/col332 {0.843 0.843 0.843 srgb} bind def
/col333 {0.557 0.557 0.651 srgb} bind def
/col334 {0.349 0.349 0.349 srgb} bind def
/col335 {0.380 0.380 0.380 srgb} bind def
/col336 {0.000 0.396 0.000 srgb} bind def
/col337 {0.349 0.412 0.220 srgb} bind def
/col338 {0.812 0.827 0.812 srgb} bind def
/col339 {0.682 0.667 0.682 srgb} bind def
/col340 {0.557 0.557 0.651 srgb} bind def
/col341 {0.937 0.729 0.349 srgb} bind def
/col342 {0.557 0.604 0.412 srgb} bind def
/col343 {0.286 0.286 0.286 srgb} bind def
/col344 {0.380 0.396 0.380 srgb} bind def
/col345 {0.349 0.412 0.220 srgb} bind def
/col346 {0.812 0.827 0.812 srgb} bind def
/col347 {0.682 0.667 0.682 srgb} bind def
/col348 {0.557 0.557 0.651 srgb} bind def
/col349 {0.937 0.729 0.349 srgb} bind def
/col350 {0.557 0.604 0.412 srgb} bind def
/col351 {0.286 0.286 0.286 srgb} bind def
/col352 {0.380 0.396 0.380 srgb} bind def
/col353 {0.349 0.412 0.220 srgb} bind def
/col354 {0.812 0.827 0.812 srgb} bind def
/col355 {0.682 0.667 0.682 srgb} bind def
/col356 {0.557 0.557 0.651 srgb} bind def
/col357 {0.937 0.729 0.349 srgb} bind def
/col358 {0.557 0.604 0.412 srgb} bind def
/col359 {0.286 0.286 0.286 srgb} bind def
/col360 {0.380 0.396 0.380 srgb} bind def
/col361 {0.349 0.412 0.220 srgb} bind def
/col362 {0.812 0.827 0.812 srgb} bind def
/col363 {0.682 0.667 0.682 srgb} bind def
/col364 {0.557 0.557 0.651 srgb} bind def
/col365 {0.937 0.729 0.349 srgb} bind def
/col366 {0.557 0.604 0.412 srgb} bind def
/col367 {0.286 0.286 0.286 srgb} bind def
/col368 {0.380 0.396 0.380 srgb} bind def
/col369 {0.843 0.843 0.843 srgb} bind def
/col370 {0.557 0.557 0.651 srgb} bind def
/col371 {0.349 0.349 0.349 srgb} bind def
/col372 {0.380 0.380 0.380 srgb} bind def
/col373 {0.937 0.937 0.812 srgb} bind def
/col374 {0.969 0.682 0.349 srgb} bind def
/col375 {0.588 0.812 0.620 srgb} bind def
/col376 {0.682 0.667 0.682 srgb} bind def
/col377 {0.714 0.078 0.475 srgb} bind def
/col378 {0.525 0.525 0.525 srgb} bind def
/col379 {0.000 0.380 0.000 srgb} bind def
/col380 {0.349 0.412 0.220 srgb} bind def
/col381 {0.843 0.843 0.843 srgb} bind def
/col382 {0.557 0.557 0.651 srgb} bind def
/col383 {0.969 0.745 0.349 srgb} bind def
/col384 {0.557 0.620 0.412 srgb} bind def
/col385 {0.286 0.286 0.286 srgb} bind def
/col386 {0.380 0.380 0.380 srgb} bind def
/col387 {0.380 0.412 0.620 srgb} bind def
/col388 {0.475 0.475 0.475 srgb} bind def
/col389 {0.000 0.349 0.000 srgb} bind def
/col390 {0.906 0.443 0.443 srgb} bind def
/col391 {0.875 0.000 0.000 srgb} bind def
/col392 {1.000 0.796 0.188 srgb} bind def
/col393 {0.157 0.475 0.286 srgb} bind def
/col394 {0.875 0.157 0.125 srgb} bind def
/col395 {0.125 0.349 0.780 srgb} bind def
/col396 {0.969 0.984 0.969 srgb} bind def
/col397 {0.906 0.906 0.906 srgb} bind def
/col398 {0.000 0.380 0.286 srgb} bind def
/col399 {0.475 0.525 0.286 srgb} bind def
/col400 {0.843 0.843 0.843 srgb} bind def
/col401 {0.380 0.443 0.475 srgb} bind def
/col402 {0.906 0.745 0.475 srgb} bind def
/col403 {0.557 0.620 0.475 srgb} bind def
/col404 {0.286 0.286 0.286 srgb} bind def
/col405 {0.651 0.714 0.780 srgb} bind def
/col406 {0.412 0.412 0.588 srgb} bind def
/col407 {0.525 0.412 0.412 srgb} bind def
/col408 {0.318 0.620 0.286 srgb} bind def
/col409 {0.843 0.906 0.906 srgb} bind def
/col410 {0.318 0.380 0.380 srgb} bind def
/col411 {0.094 0.412 0.286 srgb} bind def
/col412 {0.620 0.651 0.714 srgb} bind def
/col413 {0.125 0.525 0.349 srgb} bind def
/col414 {0.000 0.380 0.000 srgb} bind def
/col415 {0.349 0.412 0.220 srgb} bind def
/col416 {0.557 0.557 0.651 srgb} bind def
/col417 {0.969 0.745 0.349 srgb} bind def
/col418 {0.557 0.620 0.412 srgb} bind def
/col419 {0.380 0.380 0.380 srgb} bind def
/col420 {0.380 0.412 0.620 srgb} bind def
/col421 {0.380 0.380 0.380 srgb} bind def
/col422 {0.349 0.412 0.220 srgb} bind def
/col423 {0.843 0.843 0.843 srgb} bind def
/col424 {0.557 0.557 0.651 srgb} bind def
/col425 {0.969 0.745 0.349 srgb} bind def
/col426 {0.557 0.620 0.412 srgb} bind def
/col427 {0.286 0.286 0.286 srgb} bind def
/col428 {0.380 0.380 0.380 srgb} bind def
/col429 {0.557 0.412 0.412 srgb} bind def
/col430 {0.349 0.349 0.349 srgb} bind def
/col431 {0.812 0.812 0.812 srgb} bind def
/col432 {0.255 0.271 0.255 srgb} bind def
/col433 {0.745 0.765 0.745 srgb} bind def
/col434 {0.412 0.427 0.412 srgb} bind def
/col435 {0.745 0.765 0.745 srgb} bind def
/col436 {0.412 0.427 0.412 srgb} bind def
/col437 {0.286 0.271 0.286 srgb} bind def
/col438 {0.557 0.557 0.557 srgb} bind def
/col439 {0.412 0.427 0.412 srgb} bind def
/col440 {0.557 0.557 0.557 srgb} bind def
/col441 {0.188 0.188 0.188 srgb} bind def
/col442 {0.588 0.573 0.588 srgb} bind def
/col443 {0.443 0.443 0.443 srgb} bind def
/col444 {0.349 0.333 0.349 srgb} bind def
/col445 {0.682 0.698 0.682 srgb} bind def
/col446 {0.745 0.765 0.745 srgb} bind def
/col447 {0.286 0.271 0.286 srgb} bind def
/col448 {0.412 0.427 0.412 srgb} bind def
/col449 {0.286 0.271 0.286 srgb} bind def
/col450 {0.412 0.427 0.412 srgb} bind def
/col451 {0.745 0.765 0.745 srgb} bind def
/col452 {0.412 0.427 0.412 srgb} bind def
/col453 {0.286 0.271 0.286 srgb} bind def
/col454 {0.745 0.765 0.745 srgb} bind def
/col455 {0.412 0.427 0.412 srgb} bind def
/col456 {0.745 0.765 0.745 srgb} bind def
/col457 {0.286 0.271 0.286 srgb} bind def
/col458 {0.557 0.557 0.557 srgb} bind def

end
save
newpath 0 275 moveto 0 0 lineto 271 0 lineto 271 275 lineto closepath clip newpath
-31.0 304.0 translate
1 -1 scale

/cp {closepath} bind def
/ef {eofill} bind def
/gr {grestore} bind def
/gs {gsave} bind def
/sa {save} bind def
/rs {restore} bind def
/l {lineto} bind def
/m {moveto} bind def
/rm {rmoveto} bind def
/n {newpath} bind def
/s {stroke} bind def
/sh {show} bind def
/slc {setlinecap} bind def
/slj {setlinejoin} bind def
/slw {setlinewidth} bind def
/srgb {setrgbcolor} bind def
/rot {rotate} bind def
/sc {scale} bind def
/sd {setdash} bind def
/ff {findfont} bind def
/sf {setfont} bind def
/scf {scalefont} bind def
/sw {stringwidth} bind def
/tr {translate} bind def
/tnt {dup dup currentrgbcolor
  4 -2 roll dup 1 exch sub 3 -1 roll mul add
  4 -2 roll dup 1 exch sub 3 -1 roll mul add
  4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb}
  bind def
/shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul
  4 -2 roll mul srgb} bind def
 /DrawEllipse {
	/endangle exch def
	/startangle exch def
	/yrad exch def
	/xrad exch def
	/y exch def
	/x exch def
	/savematrix mtrx currentmatrix def
	x y tr xrad yrad sc 0 0 1 startangle endangle arc
	closepath
	savematrix setmatrix
	} def

/$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def
/$F2psEnd {$F2psEnteredState restore end} def

$F2psBegin
%%Page: 1 1
10 setmiterlimit
 0.06000 0.06000 sc
%
% Fig objects follow
%
15.000 slw
% Ellipse
n 2741 3384 2042 301 0 360 DrawEllipse gs col0 s gr

% Polyline
n 623 3008 m 4858 3008 l 4858 3384 l 623 3384 l
 cp gs col7 1.00 shd ef gr gs col7 s gr 
% Ellipse
n 2741 2933 2118 301 0 360 DrawEllipse gs col0 s gr

% Ellipse
n 2748 831 484 301 0 360 DrawEllipse gs col0 s gr

% Polyline
n 2120 516 m 3315 516 l 3315 871 l 2120 871 l
 cp gs col7 1.00 shd ef gr gs col7 s gr 
% Polyline
7.500 slw
n 547 2556 m 4858 2556 l 4858 2933 l 547 2933 l
 cp gs col7 1.00 shd ef gr gs col7 s gr 
15.000 slw
% Ellipse
n 2741 2692 2118 301 0 360 DrawEllipse gs col0 s gr

% Polyline
n 547 2346 m 4904 2346 l 4904 2707 l 547 2707 l
 cp gs col7 1.00 shd ef gr gs col7 s gr 
% Polyline
7.500 slw
n 2445 1135 m 2565 1135 l 2565 1015 l 2445 1015 l
 cp gs col7 1.00 shd ef gr gs col0 s gr 
% Polyline
 [60] 0 sd
n 4858 2632 m 5009 2632 l 5009 2782 l 4858 2782 l
 cp gs col7 1.00 shd ef gr gs col7 s gr  [] 0 sd
 [60] 0 sd
% Ellipse
n 2738 3359 2077 323 0 360 DrawEllipse gs col0 s gr
 [] 0 sd
% Polyline
 [15 60] 60 sd
n 2643 1114 m 1926 2425 l
 2841 946 l gs col0 s gr  [] 0 sd
% Polyline
 [15 45] 45 sd
n 2646 1117 m 2841 949 l 3600 3665 l
 cp gs col0 s gr  [] 0 sd
% Polyline
n 2657 2891 m
 2741 2891 l gs col0 s gr 
% Polyline
 [15 45] 45 sd
n 2430 3855 m
 2790 2025 l gs col0 s gr  [] 0 sd
% Polyline
 [15 45] 45 sd
n 1147 3287 m 4327 3287 l 2430 3855 l 1147 3287 l 2790 2025 l
 4327 3287 l gs col0 s gr  [] 0 sd
% Polyline
n 2698 2849 m
 2698 2933 l gs col0 s gr 
15.000 slw
% Ellipse
n 2741 2933 2118 2106 0 360 DrawEllipse gs col0 s gr

/Times-Bold ff 180.00 scf sf
2758 2854 m
gs 1 -1 sc (0) col0 sh gr
7.500 slw
 [60] 0 sd
% Ellipse
n 2741 2933 2118 301 0 360 DrawEllipse gs col0 s gr
 [] 0 sd
% Polyline
 [15 45] 45 sd
n 3602 3665 m
 1926 2425 l gs col0 s gr  [] 0 sd
% Ellipse
n 2643 1116 65 65 0 360 DrawEllipse gs col7 1.00 shd ef gr gs col0 s gr

% Polyline
n 2497 1100 m 2571 1026 l 2645 1100 l 2571 1174 l
 cp gs col7 1.00 shd ef gr gs col0 s gr 
% Polyline
 [36] 0 sd
n 2795 1922 m 2705 2076 l 2884 2076 l
 cp gs col7 0.70 shd ef gr gs col0 s gr  [] 0 sd
% Polyline
 [36] 0 sd
n 1152 3182 m 1062 3336 l 1241 3336 l
 cp gs col7 0.70 shd ef gr gs col0 s gr  [] 0 sd
% Polyline
n 2431 3752 m 2341 3906 l 2520 3906 l
 cp gs col7 0.70 shd ef gr gs col0 s gr 
% Polyline
 [36] 0 sd
n 3477 3120 m 3597 3120 l 3597 3000 l 3477 3000 l
 cp gs col7 1.00 shd ef gr gs col0 s gr  [] 0 sd
% Polyline
 [36] 0 sd
n 4325 3182 m 4235 3336 l 4414 3336 l
 cp gs col7 0.70 shd ef gr gs col0 s gr  [] 0 sd
% Arc
 [60] 0 sd
n 2771.5 -687.0 1647.1 107.4 73.5 arcn
gs col0 s gr
 [] 0 sd
 [60] 0 sd
% Ellipse
n 2748 2693 2112 301 0 360 DrawEllipse gs col0 s gr
 [] 0 sd
 [36] 0 sd
% Ellipse
n 2840 949 65 65 0 360 DrawEllipse gs col7 1.00 shd ef gr gs col0 s gr
 [] 0 sd
% Polyline
 [36] 0 sd
n 2925 997 m 3045 997 l 3045 877 l 2925 877 l
 cp gs col7 1.00 shd ef gr gs col0 s gr  [] 0 sd
 [36] 0 sd
% Ellipse
n 1926 2425 65 65 0 360 DrawEllipse gs col7 1.00 shd ef gr gs col0 s gr
 [] 0 sd
% Polyline
n 1875 3028 m 1995 3028 l 1995 2908 l 1875 2908 l
 cp gs col7 1.00 shd ef gr gs col0 s gr 
% Polyline
 [36] 0 sd
n 2842 956 m 2916 882 l 2990 956 l 2916 1030 l
 cp gs col7 1.00 shd ef gr gs col0 s gr  [] 0 sd
% Polyline
n 4771 2686 m 4845 2612 l 4919 2686 l 4845 2760 l
 cp gs col7 1.00 shd ef gr gs col0 s gr 
% Ellipse
n 3597 3660 65 65 0 360 DrawEllipse gs col7 1.00 shd ef gr gs col0 s gr

% Polyline
n 598 3383 m 672 3309 l 746 3383 l 672 3457 l
 cp gs col7 1.00 shd ef gr gs col0 s gr 
$F2psEnd
rs

%%EndDocument
 @endspecial 299 1664 a Ft(Figure)37 b(2.)49 b Fu(Placemen)m(t)34
b(of)f(p)s(oin)m(ts)g(of)f(colours)h(1)p Fs(;)17 b Fu(2)p
Fs(;)g Fu(3)32 b(and)g(an)m(tip)s(o)s(des)i(of)e(colour)g(4)h(in)299
1780 y(the)g(3-dimensional)g FA(S)1147 1744 y Fj(\000)1207
1780 y Fu(.)100 2040 y(The)25 b(construction)h(can)f(no)m(w)h(b)s(e)f
(completed.)42 b(T)-8 b(ak)m(e)26 b Fn(\000)p Fs(p)2190
2055 y Fo(2)2254 2040 y Fu(to)f(b)s(e)g(the)g(midp)s(oin)m(t)g(of)g
(shortest)h(spherical)0 2156 y(segmen)m(t)37 b(b)s(et)m(w)m(een)g
(Capricorn)f(and)f Fs(p)1458 2171 y Fo(1)1533 2156 y
Fu(\(whic)m(h)h(lies)h(b)s(elo)m(w)f(Capricorn\).)52
b(Let)35 b Fs(z)i(<)32 b Fn(\000)p Fu(2)p Fs(\017)k Fu(b)s(e)f(the)h
(\014nal)0 2272 y(co)s(ordinate)46 b(of)f Fn(\000)p Fs(p)743
2287 y Fo(2)829 2272 y Fu(and)h(arrange)f(the)h(remaining)h(p)s(oin)m
(ts)f(so)g(that)g Fn(\000)p Fs(p)2837 2287 y Fo(2)2877
2272 y Fs(;)17 b Fn(\000)p Fs(p)3047 2287 y Fo(3)3086
2272 y Fs(;)g(:)g(:)g(:)f(;)h Fn(\000)p Fs(p)3431 2287
y Fq(d)p Fo(+1)3608 2272 y Fu(form)45 b(a)0 2389 y(regular)29
b(simplex)j(on)d Fr(S)867 2353 y Fq(d)923 2389 y Fn(\\)15
b(f)p Fs(x)29 b Fn(2)f Fr(R)1304 2353 y Fq(d)1344 2389
y Fn(j)p Fs(x)1427 2404 y Fq(d)1496 2389 y Fu(=)f Fs(z)t
Fn(g)p Fu(.)43 b(Then)31 b FA(0)e Fu(is)h(in)f(the)h(con)m(v)m(ex)i(h)m
(ull)e(of)f(the)g Fn(\000)p Fs(p)3379 2404 y Fq(i)3437
2389 y Fu(\(and)h(hence)0 2505 y Fs(S)66 2464 y Fj(\000)60
2533 y Fq(d)p Fo(+1)191 2505 y Fu(\).)40 b(Finally)26
b(w)m(e)g(can)f(calculate)h FA(depth)1608 2528 y Fh(S)1653
2510 y Fe(\000)1710 2505 y Fu(\()p FA(0)p Fu(\))e(from)h(the)g(lo)s
(cation)g(of)f(the)i Fn(\000)p Fs(p)3003 2520 y Fq(i)3031
2505 y Fu(:)40 b FA(0)25 b Fu(lies)h(in)f(1)6 b(+)g Fs(d)p
Fu(\()p Fs(d)g Fn(\000)g Fu(1\))0 2621 y(colourful)28
b(simplices)j(generated)e(with)g Fs(p)1515 2636 y Fo(1)1583
2621 y Fu(and)f(one)h(simplex)h(eac)m(h)f(including)h
Fs(p)2977 2636 y Fo(2)3016 2621 y Fs(;)17 b(p)3109 2636
y Fo(3)3148 2621 y Fs(;)g(:)g(:)g(:)f(;)h(p)3416 2636
y Fq(d)p Fo(+1)3546 2621 y Fu(.)43 b(Hence:)1088 2798
y FA(depth)1370 2821 y Fh(S)1415 2802 y Fe(\000)1471
2798 y Fu(\()p FA(0)p Fu(\))28 b(=)f(1)22 b(+)g Fs(d)p
Fu(\()p Fs(d)g Fn(\000)g Fu(1\))g(+)g Fs(d)27 b Fu(=)h
Fs(d)2604 2756 y Fo(2)2665 2798 y Fu(+)22 b(1)0 2983
y Fp(R)-5 b(emark)53 b Fu(3.8)p Fp(.)46 b Fu(There)d(are)f(other)g
(nice)h(con\014gurations)f(with)h FA(depth)2669 3007
y Fh(S)2714 2988 y Fe(\000)2771 2983 y Fu(\()p FA(0)p
Fu(\))g(=)g Fs(d)3116 2947 y Fo(2)3184 2983 y Fu(+)28
b(1.)71 b(Consider)43 b(a)0 3099 y(con\014guration)f
FA(S)662 3063 y Fj(0)727 3099 y Fu(similar)h(to)f FA(S)1248
3063 y Fj(\000)1349 3099 y Fu(but)g(with)h(the)f(tropics)h(pushed)g(to)
f(the)g(north,)i(taking)e(Cancer's)0 3216 y(\014nal)30
b(co)s(ordinate)f(to)g(3)p Fs(\017)h Fu(and)f(Capricorn's)i(to)e
Fn(\000)p Fs(\017)p Fu(.)44 b(W)-8 b(e)29 b(can)h(then)g(mo)m(v)m(e)h
(eac)m(h)g(of)d Fn(\000)p Fs(p)3189 3231 y Fo(1)3229
3216 y Fs(;)17 b(:)g(:)g(:)f(;)h Fn(\000)p Fs(p)3574
3231 y Fq(d)3644 3216 y Fu(across)0 3332 y(Capricorn)45
b(and)f(the)g(equator)h(through)f(a)g(single)h(b)s(oundary)f(facet.)78
b(Finally)45 b(place)g Fn(\000)p Fs(p)3459 3347 y Fq(d)p
Fo(+1)3634 3332 y Fu(at)f(the)0 3448 y(South)31 b(P)m(ole.)44
b(Using)32 b(the)g(same)g(analysis)g(as)f(ab)s(o)m(v)m(e,)i(w)m(e)f(ha)
m(v)m(e)g Fs(p)2416 3463 y Fo(1)2456 3448 y Fs(;)17 b(:)g(:)g(:)f(;)h
(p)2724 3463 y Fq(d)2795 3448 y Fu(p)s(oin)m(ts)32 b(forming)f(1)19
b(+)g(\()p Fs(d)g Fn(\000)g Fu(1\))0 3564 y(simplices)35
b(con)m(taining)e FA(0)p Fu(,)g(and)f Fs(p)1241 3579
y Fq(d)p Fo(+1)1405 3564 y Fu(forming)g(one)h(suc)m(h)h(simplex)g(for)e
(a)h(total)f(of)g Fs(d)3145 3528 y Fo(2)3206 3564 y Fu(+)22
b(1.)100 3681 y(Both)33 b FA(S)405 3644 y Fj(\000)498
3681 y Fu(and)h FA(S)751 3644 y Fj(0)809 3681 y Fu(ha)m(v)m(e)h
(symmetry)h(for)d(the)h(\014rst)g Fs(d)g Fu(colours,)g(but)g(not)g(the)
g(last)g(one.)48 b(W)-8 b(e)34 b(can)g(also)0 3797 y(prop)s(ose)d(a)f
(con\014guration)h FA(S)1089 3761 y Fj(00)1162 3797 y
Fu(with)g(symmetry)i(b)s(et)m(w)m(een)f(all)f(the)g(colours.)43
b(F)-8 b(ollo)m(w)30 b(the)h(recip)s(e)h(for)e FA(S)3841
3761 y Fj(\000)0 3913 y Fu(but)i(place)g(one)f(p)s(oin)m(t)h(of)f(eac)m
(h)h(colour)f(on)g(Cancer)i(and)e(Capricorn)h(and)g(place)g(the)f
(remaining)h(p)s(oin)m(ts)0 4029 y(in)44 b(the)h(p)s(olar)e(region.)78
b(This)45 b(brings)f(a)g(n)m(um)m(b)s(er)h(of)f(tec)m(hnical)h
(di\016culties,)k(ho)m(w)m(ev)m(er.)80 b(The)45 b(p)s(oin)m(ts)0
4145 y(will)38 b(not)g(b)s(e)g(in)g(general)g(p)s(osition,)h(since)g
(the)f(tropical)g(h)m(yp)s(erplanes)i(include)f(\()p
Fs(d)25 b Fu(+)h(1\))37 b(p)s(oin)m(ts.)60 b(It)37 b(is)0
4262 y(also)k(a)g(bit)g(less)i(natural)e(to)g(ev)m(enly)i(space)f(\()p
Fs(d)28 b Fu(+)f(1\))41 b(p)s(oin)m(ts)h(on)f(copies)h(of)f
Fr(S)2964 4226 y Fq(d)p Fj(\000)p Fo(1)3095 4262 y Fu(,)i(indeed)g(for)
d Fs(d)i Fu(=)g(2)0 4378 y(this)37 b(construction)h(do)s(es)f(not)f
(mak)m(e)h(sense.)57 b(When)38 b(there)f(is)g(a)f(nice)h(w)m(a)m(y)h
(to)e(do)g(this)i(for)d Fs(d)f Fn(\025)h Fu(3)h(this)0
4494 y(\(e.g.)i(4)f(p)s(oin)m(ts)h(on)g Fr(S)802 4458
y Fo(2)841 4494 y Fu(\))g(w)m(e)g(ma)m(y)h(end)f(up)g(with)g(some)h(p)s
(oin)m(ts)f(b)s(eing)g(an)m(tip)s(o)s(des.)59 b(This)38
b(w)m(ould)h(cause)0 4610 y FA(0)e Fu(to)g(b)s(e)g(on)g(the)g(faces)h
(of)e(some)i(simplices)h(and)e(increase)i(its)e(colourful)g(simplicial)
i(depth.)57 b(Most)37 b(of)0 4727 y(these)32 b(problems)g(can)f(b)s(e)g
(\014xed)h(b)m(y)g(p)s(erturbing)f FA(S)1885 4690 y Fj(00)1928
4727 y Fu(,)g(but)g(ev)m(en)i(so)d FA(S)2563 4690 y Fj(00)2637
4727 y Fu(is)h(not)g(w)m(ell-suited)i(to)d(our)h(pro)s(of)0
4843 y(tec)m(hnique.)46 b(One)33 b(migh)m(t)g(also)g(consider)g
(con\014gurations)h(that)e(are)h(not)f(con\014ned)i(to)e(the)h(sphere.)
0 5028 y(3.5.)49 b FA(Ev)-6 b(aluating)38 b Fs(\026)p
Fu(\()p Fs(d)p Fu(\))p FA(.)49 b Fu(The)34 b(con\014guration)f
FA(S)1880 4992 y Fj(\000)1973 5028 y Fu(of)f(Section)i(3.4)f
(satis\014es)i(m\()p FA(S)3125 4992 y Fj(\000)3185 5028
y Fu(\))28 b Fn(\024)i Fs(d)3409 4992 y Fo(2)3470 5028
y Fu(+)23 b(1)33 b(where)0 5145 y(m\()p FA(S)p Fu(\))h(is)g(the)g
(minim)m(um)h(colourful)f(simplicial)h(depth)f(of)f(core)h(p)s(oin)m(t)
g(de\014ned)h(in)e(\(6\).)46 b(W)-8 b(e)34 b(w)m(ould)h(lik)m(e)0
5261 y(to)30 b(pro)m(v)m(e)h(that)f(m)q(\()p FA(S)768
5225 y Fj(\000)827 5261 y Fu(\))e(=)f Fs(d)1047 5225
y Fo(2)1104 5261 y Fu(+)17 b(1)30 b(and)g(in)h(fact)f(that)g(for)f(an)m
(y)i(colourful)g(con\014guration)f FA(S)g Fu(w)m(e)i(will)f(ha)m(v)m(e)
p eop end
%%Page: 11 11
TeXDict begin 11 10 bop 1304 71 a Fl(COLOURFUL)32 b(SIMPLICIAL)g(DEPTH)
1227 b(11)0 274 y Fu(m\()p FA(S)p Fu(\))37 b Fn(\025)h
Fs(d)422 238 y Fo(2)487 274 y Fu(+)26 b(1,)39 b(or)f(equiv)-5
b(alen)m(tly)40 b Fs(\026)p Fu(\()p Fs(d)p Fu(\))c Fn(\025)i
Fs(d)1764 238 y Fo(2)1829 274 y Fu(+)26 b(1.)59 b(The)39
b(second)h(half)d(of)h(this)h(prop)s(osition)f(clearly)0
390 y(implies)d(the)f(\014rst.)46 b(W)-8 b(e)34 b(suggest)g(it)f(is)h
(also)f(more)h(approac)m(hable)g(since)h(w)m(e)f(can)g(mo)m(v)m(e)g
(the)g(core)g(p)s(oin)m(t)0 506 y(of)41 b(minim)m(um)j(depth)e(to)g
FA(0)g Fu(during)g(prepro)s(cessing,)k(whereas)d(a)e(direct)i(attac)m
(k)f(on)g(m\()p FA(S)3427 470 y Fj(\000)3487 506 y Fu(\))f(requires)0
623 y(understanding)34 b(the)f(shap)s(e)g(of)f(the)h(core)g(of)f
FA(S)1740 586 y Fj(\000)1800 623 y Fu(.)100 739 y(B\023)-49
b(ar\023)g(an)m(y's)39 b(original)f(Colourful)g(Carath)m(\023)-46
b(eo)s(dory)39 b(theorem)g(is)g(exactly)g(that)f Fs(\026)p
Fu(\()p Fs(d)p Fu(\))f Fn(\025)h Fu(1.)60 b(He)39 b(further)0
855 y(sho)m(ws)30 b(that)d(for)h(an)m(y)g FA(S)h Fu(an)m(y)f(colourful)
g(p)s(oin)m(t)g(from)g FA(S)g Fu(is)h(part)e(of)h(some)h(generating)f
(set)h(for)e(a)h(colourful)0 971 y(simplex)e(con)m(taining)f
FA(0)p Fu(.)41 b(This)25 b(immediately)h(yields)g Fs(\026)p
Fu(\()p Fs(d)p Fu(\))h Fn(\025)h Fs(d)5 b Fu(+)g(1.)40
b(In)24 b FA(S)2710 935 y Fj(\000)2794 971 y Fu(w)m(e)h(see)g(that)f
Fs(p)3330 986 y Fo(2)3370 971 y Fs(;)17 b(p)3463 986
y Fo(3)3502 971 y Fs(;)g(:)g(:)g(:)f(;)h(p)3770 986 y
Fq(d)p Fo(+1)0 1087 y Fu(all)27 b(generate)h(a)f Fp(unique)g
Fu(colourful)g(simplex)i(con)m(taining)f FA(0)p Fu(.)42
b(Th)m(us)28 b(the)g(minim)m(um)h(n)m(um)m(b)s(er)f(of)f(colourful)0
1204 y(simplices)46 b(con)m(taining)e FA(0)f Fu(generated)h(b)m(y)g(an)
f(arbitrary)g(p)s(oin)m(t)h(in)f(a)g(con\014guration)h(is)f(1.)76
b(T)-8 b(o)43 b(get)g(a)0 1320 y(stronger)f(lo)m(w)m(er)g(b)s(ound)g
(than)f Fs(\026)p Fu(\()p Fs(d)p Fu(\))h Fn(\025)h Fs(d)28
b Fu(+)g(1)41 b(w)m(e)i(need)f(to)f(understand)i(some)f(global)f
(information)0 1436 y(ab)s(out)32 b(con\014gurations.)0
1601 y FA(Lemma)k(3.9.)k Fp(Fix)32 b(the)g(sets)h Fs(S)1188
1616 y Fo(1)1227 1601 y Fs(;)17 b(:)g(:)g(:)f(;)h(S)1506
1616 y Fq(d)1579 1601 y Fp(fr)-5 b(om)32 b(a)g(c)-5 b(olourful)32
b(c)-5 b(on\014gur)g(ation)32 b FA(S)h Fp(with)f FA(0)g
Fp(in)h(its)f(c)-5 b(or)g(e,)33 b(and)0 1717 y(c)-5 b(onsider)31
b(the)i(c)-5 b(el)5 b(ls)32 b(cr)-5 b(e)g(ate)g(d)32
b(on)g Fr(S)1271 1681 y Fq(d)1344 1717 y Fp(by)g(the)h(c)-5
b(olourful)32 b(simplicial)f(c)-5 b(ones)32 b(fr)-5 b(om)32
b(these)g(sets.)43 b(Then)32 b(every)0 1833 y(c)-5 b(el)5
b(l)34 b(has)f(depth)h(at)g(le)-5 b(ast)34 b(1,)g(and)g(if)g(ther)-5
b(e)34 b(is)g(a)g(c)-5 b(el)5 b(l)34 b(of)f(depth)h(1)g(it)h(is)f
(unique)g(and)f(al)5 b(l)34 b(other)g(c)-5 b(el)5 b(ls)34
b(have)0 1950 y(depth)h(at)g(le)-5 b(ast)34 b Fs(d)p
Fp(.)0 2114 y(Pr)-5 b(o)g(of.)41 b Fu(The)47 b(fact)e(that)h(ev)m(ery)h
(cell)g(has)f(depth)h(at)e(least)h(1)g(is)g(equiv)-5
b(alen)m(t)48 b(to)d(the)h(fact)g(that)f(ev)m(ery)0 2231
y(colourful)27 b(p)s(oin)m(t)h(generates)g(some)g(colourful)g(simplex)h
(that)e(con)m(tains)h FA(0)p Fu(,)h(pro)m(v)m(ed)f(in)g([B\023)-49
b(ar82)o(].)42 b(Supp)s(ose)0 2347 y(no)m(w)34 b(that)g(there)g(is)h(a)
e(cell)i Fs(C)40 b Fu(of)34 b(depth)g(1.)47 b(An)m(y)35
b(p)s(oin)m(t)f(exiting)g Fs(C)41 b Fu(through)34 b(a)f(b)s(ounding)h
(h)m(yp)s(erplane)0 2463 y(will)40 b(b)s(e)g(exiting)h(some)g
(colourful)e(simplex.)67 b(Since)41 b(the)f(depth)h(of)e
Fs(C)47 b Fu(is)40 b(1,)h(this)g(will)f(alw)m(a)m(ys)i(b)s(e)e(the)0
2579 y(same)35 b(simplex.)49 b(Th)m(us)35 b(the)f(extreme)i(p)s(oin)m
(ts)e(of)f Fs(C)41 b Fu(m)m(ust)35 b(b)s(e)f(a)f(colourful)h(set)h
Fs(A)30 b Fu(=)f Fn(f)p Fs(a)3277 2594 y Fo(1)3317 2579
y Fs(;)17 b(:)g(:)g(:)e(;)i(a)3586 2594 y Fq(d)3627 2579
y Fn(g)33 b Fu(with)0 2695 y Fs(a)51 2710 y Fq(i)120
2695 y Fn(2)40 b Fs(S)286 2710 y Fq(i)355 2695 y Fu(generating)g(this)g
(simplex.)68 b(W)-8 b(e)41 b(can)f(puncture)h Fr(S)2288
2659 y Fq(d)2369 2695 y Fu(at)f Fs(p)g Fn(2)g Fs(C)47
b Fu(and)40 b(pro)5 b(ject)41 b Fr(S)3401 2659 y Fq(d)3469
2695 y Fn(n)27 b(f)p Fs(p)p Fn(g)40 b Fu(in)m(to)0 2812
y Fr(R)72 2776 y Fq(d)p Fj(\000)p Fo(1)203 2812 y Fu(.)j(The)34
b Fs(a)525 2827 y Fq(i)553 2812 y Fu('s)f(pro)5 b(ject)34
b(to)e(a)g(set)h Fs(A)1410 2776 y Fj(0)1462 2812 y Fu(=)27
b Fn(f)p Fs(a)1666 2776 y Fj(0)1666 2836 y Fo(1)1706
2812 y Fs(;)17 b(:)g(:)g(:)e(;)i(a)1975 2776 y Fj(0)1975
2838 y Fq(d)2016 2812 y Fn(g)32 b Fu(that)h(forms)f(a)h(\()p
Fs(d)22 b Fn(\000)g Fu(1\)-simplex)34 b(in)f Fr(R)3531
2776 y Fq(d)p Fj(\000)p Fo(1)3661 2812 y Fu(.)44 b(The)0
2928 y(remaining)33 b(colourful)g(p)s(oin)m(ts)g(pro)5
b(ject)33 b(to)g(p)s(oin)m(ts)g(in)g(con)m(v)r(\()p Fs(A)2319
2892 y Fj(0)2343 2928 y Fu(\).)100 3044 y(T)-8 b(ak)m(e)29
b(a)e(p)s(oin)m(t)h Fs(q)k Fu(inside)d(con)m(v)s(\()p
Fs(A)1312 3008 y Fj(0)1335 3044 y Fu(\).)42 b(W)-8 b(e)28
b(w)m(an)m(t)h(to)f(sho)m(w)h(that)f Fs(q)j Fu(is)e(con)m(tained)g(in)f
(at)g(least)g Fs(d)g Fu(colourful)0 3160 y(simplices)e(in)f(addition)f
(to)g(con)m(v)r(\()p Fs(A)1304 3124 y Fj(0)1327 3160
y Fu(\))g(after)g(pro)5 b(jection.)41 b(T)-8 b(o)24 b(do)g(this,)j(it)d
(is)g(su\016cien)m(t)i(to)e(sho)m(w)h(that)f(if)g(w)m(e)0
3277 y(tak)m(e)i(an)m(y)g(colourful)f(set)h Fs(B)1001
3240 y Fj(0)1052 3277 y Fu(=)h Fn(f)p Fs(b)1246 3240
y Fj(0)1246 3301 y Fo(1)1286 3277 y Fs(;)17 b(:)g(:)g(:)f(;)h(b)1546
3240 y Fj(0)1546 3303 y Fq(d)1587 3277 y Fn(g)24 b Fu(of)h(pro)5
b(jected)26 b(p)s(oin)m(ts)g(with)g Fs(b)2730 3240 y
Fj(0)2730 3301 y Fq(i)2784 3277 y Fu(of)e(colour)h Fs(i)h
Fu(and)f Fs(A)3486 3240 y Fj(0)3516 3277 y Fn(\\)7 b
Fs(B)3668 3240 y Fj(0)3720 3277 y Fu(=)27 b Fn(;)p Fu(,)0
3393 y(then)37 b Fs(q)j Fu(is)d(in)f(some)h(colourful)f(simplex)i
(generated)g(from)d(p)s(oin)m(ts)i(of)f Fs(A)2709 3357
y Fj(0)2757 3393 y Fn([)25 b Fs(B)2927 3357 y Fj(0)2987
3393 y Fu(with)36 b(some)h(generators)0 3509 y(from)45
b Fs(B)322 3473 y Fj(0)345 3509 y Fu(.)81 b(Equiv)-5
b(alen)m(tly)d(,)51 b(w)m(e)46 b(w)m(an)m(t)f(to)g(sho)m(w)h(that)f
(con)m(v)s(\()p Fs(A)2377 3473 y Fj(0)2400 3509 y Fu(\))g(is)g(co)m(v)m
(ered)i(b)m(y)f(colourful)g(simplices)0 3625 y(generated)35
b(from)f Fs(A)751 3589 y Fj(0)797 3625 y Fn([)24 b Fs(B)966
3589 y Fj(0)1023 3625 y Fu(\(excluding)36 b(con)m(v)r(\()p
Fs(A)1806 3589 y Fj(0)1830 3625 y Fu(\))e(itself)g(from)g(the)h(co)m(v)
m(ering\).)49 b(Then)35 b(b)m(y)g(partitioning)0 3742
y(the)k(pro)5 b(jections)40 b(of)f(the)g(colourful)g(p)s(oin)m(ts)g(in)
m(to)g(\()p Fs(d)27 b Fu(+)f(1\))38 b(colourful)h(sets)h
Fs(A)2910 3705 y Fj(0)2934 3742 y Fs(;)17 b(B)3057 3705
y Fj(0)3052 3766 y Fo(1)3091 3742 y Fs(;)g(B)3214 3705
y Fj(0)3209 3766 y Fo(2)3248 3742 y Fs(;)g(:)g(:)g(:)f(;)h(B)3546
3705 y Fj(0)3541 3767 y Fq(d)3620 3742 y Fu(w)m(e)40
b(get)0 3858 y(Lemma)33 b(3.9.)100 3974 y(Consider)28
b(the)e(collection)i(X)e(of)g(colourful)h(\()p Fs(d)10
b Fn(\000)g Fu(1\)-simplices)27 b(generated)h(b)m(y)f
Fs(A)3044 3938 y Fj(0)3094 3974 y Fu(and)f Fs(B)3356
3938 y Fj(0)3406 3974 y Fu(in)h Fr(R)3586 3938 y Fq(d)p
Fj(\000)p Fo(1)3743 3974 y Fu(and)0 4099 y(let)164 4073
y(~)136 4099 y Fs(X)35 b Fu(b)s(e)28 b(the)g(set)g(of)f(p)s(oin)m(ts)i
(con)m(tained)f(in)g(the)g(colourful)g(simplices)i(of)d
Fs(X)35 b Fu(other)28 b(than)f(con)m(v)s(\()p Fs(A)3602
4062 y Fj(0)3625 4099 y Fu(\).)42 b(The)0 4215 y(elemen)m(ts)28
b(of)e(X)g(are)h(all)f(the)g(simplices)j(formed)d(b)m(y)h(taking)g(for)
e(eac)m(h)i(colour)g Fs(i)h Fu(=)f(1)p Fs(;)17 b Fu(2)p
Fs(;)g(:)g(:)g(:)e(;)i(d)26 b Fu(either)h Fs(a)3759 4179
y Fj(0)3759 4239 y Fq(i)3813 4215 y Fu(or)0 4331 y Fs(b)41
4295 y Fj(0)41 4356 y Fq(i)105 4331 y Fu(as)36 b(a)g(generating)g(v)m
(ertex.)54 b(This)37 b(construction)g(resem)m(bles)i(the)d
Fs(d)p Fu(-dimensional)g(cross-p)s(olytop)s(e)g Fs(\014)3859
4346 y Fq(d)0 4447 y Fu(\(the)31 b(dual)h(of)e(the)i
Fs(d)p Fu(-cub)s(e\),)f(a)g(regular)g(p)s(olytop)s(e)g(in)g
Fr(R)2068 4411 y Fq(d)2139 4447 y Fu(with)h(2)p Fs(d)e
Fu(v)m(ertices)k(and)d(2)3079 4411 y Fq(d)3150 4447 y
Fu(facets.)44 b(The)31 b(cross-)0 4563 y(p)s(olytop)s(e)36
b Fs(\014)462 4578 y Fq(d)538 4563 y Fu(is)g(generated)h(b)m(y)f
(taking)g(as)g(v)m(ertices)i(the)e(standard)g(unit)g(v)m(ectors)i
Fs(E)3211 4527 y Fo(+)3303 4563 y Fu(=)33 b Fn(f)p Fs(e)3507
4578 y Fo(1)3546 4563 y Fs(;)17 b(:)g(:)g(:)f(;)h(e)3810
4578 y Fq(d)3850 4563 y Fn(g)0 4680 y Fu(and)36 b(their)h(negativ)m(es)
h Fs(E)935 4644 y Fj(\000)1028 4680 y Fu(=)c Fn(f\000)p
Fs(e)1310 4695 y Fo(1)1350 4680 y Fs(;)17 b(:)g(:)g(:)f(;)h
Fn(\000)p Fs(e)1691 4695 y Fq(d)1732 4680 y Fn(g)p Fu(.)54
b(The)37 b(facets)g(of)f Fs(\014)2515 4695 y Fq(d)2592
4680 y Fu(are)g(the)h(con)m(v)m(ex)i(h)m(ulls)e(generated)0
4796 y(b)m(y)c(c)m(ho)s(osing)h(for)e(eac)m(h)h Fs(i)28
b Fu(=)g(1)p Fs(;)17 b(:)g(:)g(:)e(;)i(d)32 b Fu(either)i
Fs(e)1737 4811 y Fq(i)1797 4796 y Fu(or)f Fn(\000)p Fs(e)2039
4811 y Fq(i)2068 4796 y Fu(.)100 4912 y(W)-8 b(e)26 b(can)h(see)g(that)
f(X)h(is)f(obtained)h(from)f Fs(\014)1655 4927 y Fq(d)1722
4912 y Fu(as)g(follo)m(ws:)41 b(W)-8 b(e)27 b(ha)m(v)m(e)h
Fs(A)2644 4876 y Fj(0)2676 4912 y Fn([)9 b Fs(B)2830
4876 y Fj(0)2882 4912 y Fn(\032)28 b Fr(R)3059 4876 y
Fq(d)p Fj(\000)p Fo(1)3190 4912 y Fu(.)41 b(Em)m(b)s(ed)28
b Fr(R)3656 4876 y Fq(d)p Fj(\000)p Fo(1)3813 4912 y
Fu(as)0 5028 y(an)f(a\016ne)g(subspace)i(A\013)7 b(\()p
Fs(A)1034 4992 y Fj(0)1057 5028 y Fu(\))27 b(in)g Fr(R)1302
4992 y Fq(d)1343 5028 y Fu(.)41 b(T)-8 b(ak)m(e)28 b(H)f(to)g(b)s(e)g
(an)g(a\016ne)g(h)m(yp)s(erplane)i(in)e Fr(R)3042 4992
y Fq(d)3109 5028 y Fu(parallel)g(to)g(A\013)7 b(\()p
Fs(A)3812 4992 y Fj(0)3835 5028 y Fu(\).)0 5145 y(F)-8
b(or)34 b Fs(i)d Fu(=)f(1)p Fs(;)17 b(:)g(:)g(:)f(;)h(d)34
b Fu(let)g Fs(p)891 5160 y Fq(i)954 5145 y Fu(b)s(e)g(the)h(in)m
(tersection)i(p)s(oin)m(t)d(of)g(H)g(with)h(the)g(line)g(through)g
Fs(b)3252 5108 y Fj(0)3252 5169 y Fq(i)3315 5145 y Fu(p)s(erp)s
(endicular)0 5261 y(to)i Fr(R)196 5225 y Fq(d)p Fj(\000)p
Fo(1)326 5261 y Fu(.)57 b(Let)37 b Fs(P)49 b Fu(=)35
b Fn(f)p Fs(p)911 5276 y Fo(1)950 5261 y Fs(;)17 b(:)g(:)g(:)f(p)1174
5276 y Fq(d)1214 5261 y Fn(g)37 b Fu(and)g(generate)h(a)e(set)i
Fs(Q)f Fu(of)g(\()p Fs(d)24 b Fn(\000)i Fu(1\)-simplices)39
b(b)m(y)e(taking)h(for)e(eac)m(h)p eop end
%%Page: 12 12
TeXDict begin 12 11 bop 0 75 a Fl(12)498 b(ANTOINE)25
b(DEZA,)g(SUI)f(HUANG,)h(T)-6 b(AMON)25 b(STEPHEN)h(AND)e(T)-6
b(AM)2823 56 y(\023)2813 75 y(AS)25 b(TERLAKY)0 274 y
Fs(i)31 b Fu(=)f(1)p Fs(;)17 b(:)g(:)g(:)e(;)i(d)34 b
Fu(either)h Fs(a)851 238 y Fj(0)851 298 y Fq(i)913 274
y Fu(or)f Fs(p)1083 289 y Fq(i)1111 274 y Fu(.)48 b(By)35
b(construction)g Fs(X)42 b Fu(is)34 b(the)h(pro)5 b(jection)35
b(of)e Fs(Q)i Fu(in)m(to)f(A\013)7 b(\()p Fs(A)3429 238
y Fj(0)3452 274 y Fu(\).)48 b(No)m(w)35 b(w)m(e)0 390
y(claim)g(that)f Fs(Q)h Fu(is)g(a)g(con)m(tin)m(uous)h(image)f(of)f
(the)h(facets)g(of)f Fs(\014)2272 405 y Fq(d)2313 390
y Fu(.)49 b(W)-8 b(e)35 b(can)g(exhibit)h(suc)m(h)g(a)e(map)h(b)m(y)g
(\014rst)0 506 y(\014nding)h(an)g(a\016ne)h(transformation)e
Fs(T)1455 521 y Fo(1)1531 506 y Fu(with)h Fs(T)1813 521
y Fo(1)1853 506 y Fu(\()p Fs(e)1936 521 y Fq(i)1964 506
y Fu(\))e(=)f Fs(a)2196 470 y Fj(0)2196 531 y Fq(i)2260
506 y Fu(for)i Fs(i)f Fu(=)f(1)p Fs(;)17 b(:)g(:)g(:)f(;)h(d)35
b Fu(and)h Fs(T)3192 521 y Fo(1)3231 506 y Fu(\(A\013)7
b(\()p Fs(E)3522 470 y Fj(\000)3581 506 y Fu(\)\))34
b(=)f(H.)0 623 y(Note)h(that)g Fs(T)507 638 y Fo(1)546
623 y Fu(\()p Fs(\014)639 638 y Fq(d)680 623 y Fu(\))g(is)g(a)g(p)s
(olytop)s(e.)47 b(Then)35 b(applying)g(a)f(further)g(a\016ne)g
(transformation)g Fs(t)3409 638 y Fo(2)3483 623 y Fu(to)f(H)h(with)0
739 y Fs(t)35 754 y Fo(2)75 739 y Fu(\()p Fn(\000)p Fs(e)235
754 y Fq(i)263 739 y Fu(\))c(=)f Fs(p)485 754 y Fq(i)546
739 y Fu(for)k Fs(i)c Fu(=)g(1)p Fs(;)17 b(:)g(:)g(:)f(;)h(d)33
b Fu(and)g(extending)i(this)f(to)f Fs(T)2221 754 y Fo(2)2294
739 y Fu(on)h Fr(R)2503 703 y Fq(d)2577 739 y Fu(so)f(that)g
Fs(T)2966 754 y Fo(2)3039 739 y Fu(\014xes)i(A\013)7
b(\()p Fs(A)3508 703 y Fj(0)3532 739 y Fu(\),)33 b(w)m(e)i(see)0
855 y(that)d(the)h(comp)s(osition)h Fs(T)982 870 y Fo(2)1043
855 y Fn(\016)22 b Fs(T)1172 870 y Fo(1)1244 855 y Fu(is)33
b(the)g(required)i(map.)100 974 y(W)-8 b(e)26 b(pro)s(ceed)g(b)m(y)h
(con)m(tradiction.)42 b(Assume)27 b(that)1959 949 y(~)1931
974 y Fs(X)33 b Fu(do)s(es)26 b(not)g(co)m(v)m(er)h(con)m(v)r(\()p
Fs(A)2977 938 y Fj(0)3001 974 y Fu(\).)41 b(Then)26 b(w)m(e)h(can)f
(\014nd)g(a)0 1099 y(retraction)i(of)579 1073 y(~)551
1099 y Fs(X)35 b Fu(to)27 b(its)h(b)s(oundary)g Fs(@)5
b Fu(\(con)m(v)s(\()p Fs(A)1748 1062 y Fj(0)1772 1099
y Fu(\)\).)41 b(By)28 b(comp)s(osing)g Fs(T)2596 1114
y Fo(2)2636 1099 y Fu(,)g(the)g(pro)5 b(jection)29 b(taking)e
Fs(Q)h Fu(on)m(to)0 1223 y Fs(X)i Fu(and)22 b(the)h(retraction)f(of)
1016 1198 y(~)988 1223 y Fs(X)8 b Fu(,)24 b(w)m(e)f(get)f(a)g
(retraction)h(of)e Fs(T)2081 1238 y Fo(1)2121 1223 y
Fu(\()p Fs(\014)2214 1238 y Fq(d)2255 1223 y Fu(\))q
Fn(n)q Fu(con)m(v)r(\()p Fs(A)2652 1187 y Fj(0)2675 1223
y Fu(\))h(on)m(to)g Fs(@)5 b Fu(\(con)m(v)s(\()p Fs(A)3346
1187 y Fj(0)3370 1223 y Fu(\)\).)40 b(Ho)m(w)m(ev)m(er,)0
1339 y Fs(T)57 1354 y Fo(1)97 1339 y Fu(\()p Fs(@)5 b
Fu(\()p Fs(\014)284 1354 y Fq(d)325 1339 y Fu(\)\))36
b(is)h(a)f Fs(d)p Fu(-dimensional)h(p)s(olytop)s(e)g(top)s(ologically)f
(equiv)-5 b(alen)m(t)38 b(to)e Fr(S)2879 1303 y Fq(d)2956
1339 y Fu(and)h(hence)h Fs(T)3482 1354 y Fo(1)3521 1339
y Fu(\()p Fs(@)5 b Fu(\()p Fs(\014)3708 1354 y Fq(d)3750
1339 y Fu(\)\))24 b Fn(n)0 1455 y Fu(con)m(v)r(\()p Fs(A)307
1419 y Fj(0)331 1455 y Fu(\))34 b(is)i(top)s(ologically)e(equiv)-5
b(alen)m(t)37 b(to)d(a)h(\()p Fs(d)23 b Fn(\000)h Fu(1\)-dimensional)35
b(disk)h Fr(B)2894 1419 y Fq(d)p Fj(\000)p Fo(1)3025
1455 y Fu(.)50 b(But)35 b Fs(@)5 b Fu(\(con)m(v)t(\()p
Fs(A)3701 1419 y Fj(0)3724 1455 y Fu(\)\))34 b(is)0 1572
y(top)s(ologically)j(equiv)-5 b(alen)m(t)39 b(to)e Fr(S)1226
1536 y Fq(d)p Fj(\000)p Fo(1)1395 1572 y Fu(and)g(a)g(w)m(ell-kno)m(wn)
j(theorem)e(of)f(algebraic)h(top)s(ology)e(sa)m(ys)j(that)0
1688 y(there)26 b(do)s(es)f(not)g(exist)h(a)f(retraction)g(of)f
Fr(B)1528 1652 y Fq(d)p Fj(\000)p Fo(1)1684 1688 y Fu(to)h
Fr(S)1851 1652 y Fq(d)p Fj(\000)p Fo(1)2007 1688 y Fu(\(see)h(for)e
(example)i(section)h(21)d(of)g([Mun84)q(]\).)41 b(This)0
1804 y(is)25 b(the)f(required)i(con)m(tradiction,)g(hence)g(the)e
(colourful)g(simplices)j(of)c(X)5 b Fn(n)g Fu(con)m(v)r(\()p
Fs(A)3000 1768 y Fj(0)3024 1804 y Fu(\))24 b(co)m(v)m(er)h(con)m(v)s
(\()p Fs(A)3637 1768 y Fj(0)3660 1804 y Fu(\).)98 b Ff(\003)0
1983 y FA(Corollary)36 b(3.10.)k Fp(The)31 b(minimum)g(c)-5
b(olourful)32 b(simplicial)f(depth)h(of)g(any)g(c)-5
b(or)g(e)31 b(p)-5 b(oint)32 b(in)g(any)g(c)-5 b(olourful)0
2099 y(c)g(on\014gur)g(ation)34 b(is)h(at)g(le)-5 b(ast)34
b Fu(2)p Fs(d)p Fp(.)45 b(That)34 b(is,)h(we)f(have)g
Fs(\026)p Fu(\()p Fs(d)p Fu(\))27 b Fn(\025)h Fu(2)p
Fs(d)p Fp(.)0 2277 y(Pr)-5 b(o)g(of.)41 b Fu(It)32 b(su\016ces)h(to)e
(pro)m(v)m(e)i(this)f(for)e(a)h(con\014guration)h FA(S)f
Fu(with)h(\()p Fs(d)20 b Fu(+)f(1\))31 b(in)h(\()p Fs(d)19
b Fu(+)g(1\))31 b(colours.)44 b(Observ)m(e)0 2394 y(that)28
b(if)f(w)m(e)i(ha)m(v)m(e)h(no)d(cell)i(of)f(depth)g(1)g(then)g(eac)m
(h)h(of)f(the)g(\()p Fs(d)13 b Fu(+)g(1\))26 b(p)s(oin)m(ts)j(of)e
Fs(S)2866 2409 y Fq(d)p Fo(+1)3025 2394 y Fu(will)h(generate)h(at)e
(least)0 2510 y(t)m(w)m(o)k(colourful)g(simplices)i(con)m(taining)e
FA(0)p Fu(,)g(and)g(if)g(w)m(e)g(do)g(ha)m(v)m(e)h(suc)m(h)g(a)e(cell)h
Fs(C)7 b Fu(,)31 b(w)m(e)h(m)m(ust)g(place)f(at)f(least)0
2626 y(one)i(p)s(oin)m(t,)g(sa)m(y)h Fs(p)676 2641 y
Fo(1)743 2626 y Fn(2)28 b Fs(S)897 2641 y Fq(d)p Fo(+1)1059
2626 y Fu(outside)33 b(of)e Fs(C)39 b Fu(to)31 b(get)h
FA(0)c Fn(2)g Fu(con)m(v)r(\()p Fs(S)2366 2641 y Fq(d)p
Fo(+1)2497 2626 y Fu(\).)43 b(Then)33 b Fs(p)2908 2641
y Fo(1)2979 2626 y Fu(is)f(generates)h(at)e(least)h Fs(d)0
2742 y Fu(simplices)j(con)m(taining)e FA(0)g Fu(in)g(addition)f(to)h
(the)g Fs(d)f Fu(required)i(of)e(the)h(remaining)g(p)s(oin)m(ts)g(in)g
Fs(S)3428 2757 y Fq(d)p Fo(+1)3559 2742 y Fu(.)237 b
Ff(\003)0 2931 y Fu(3.6.)49 b FA(The)g(Tw)m(o-dimensional)j(Case.)e
Fu(W)-8 b(e)44 b(will)f(brie\015y)i(illustrate)e(our)g(metho)s(ds)h(b)m
(y)g(describing)0 3047 y(ho)m(w)f(core)f(p)s(oin)m(ts)g(can)g(b)s(e)g
(con)m(tained)h(in)f(con\014gurations)h(in)f Fr(R)2468
3011 y Fo(2)2507 3047 y Fu(.)72 b(Consider)43 b(suc)m(h)g(a)f
(con\014guration)0 3164 y FA(S)28 b Fu(=)f Fn(f)p Fs(X)r(;)17
b(Y)5 b(;)17 b(Z)7 b Fn(g)24 b Fu(with)g(core)g(p)s(oin)m(t)g
Fs(p)p Fu(.)41 b(W)-8 b(e)24 b(assume)h(general)f(p)s(osition,)i(and)e
(as)g(discussed)j(in)d(Section)g(3.1,)0 3280 y(w)m(e)31
b(ma)m(y)f(without)h(loss)f(of)g(generalit)m(y)h(tak)m(e)f(the)g(core)h
(p)s(oin)m(t)f Fs(p)d Fu(=)h FA(0)h Fu(and)h(place)h(the)f(p)s(oin)m
(ts)g(of)g FA(S)g Fu(on)g(the)0 3396 y(unit)j(circle)h
Fr(S)516 3360 y Fo(2)555 3396 y Fu(.)100 3512 y(Then)44
b(the)f(p)s(oin)m(ts)h(of)f Fs(X)51 b Fu(and)43 b Fs(Y)64
b Fu(divide)45 b Fr(S)1778 3476 y Fo(2)1861 3512 y Fu(in)m(to)e(six)h
(segmen)m(ts.)77 b(Let)44 b Fs(X)53 b Fu(=)46 b Fn(f)p
Fs(x)3261 3527 y Fo(1)3300 3512 y Fs(;)17 b(x)3399 3527
y Fo(2)3439 3512 y Fs(;)g(x)3538 3527 y Fo(3)3578 3512
y Fn(g)p Fu(,)45 b Fs(Y)67 b Fu(=)0 3629 y Fn(f)p Fs(y)98
3644 y Fo(1)137 3629 y Fs(;)17 b(y)229 3644 y Fo(2)268
3629 y Fs(;)g(y)360 3644 y Fo(3)398 3629 y Fn(g)p Fu(.)67
b(These)42 b(p)s(oin)m(ts)f(generate)g(9)f(simplicial)i(cones)f(and)g
(divide)g Fr(S)2880 3592 y Fo(2)2960 3629 y Fu(in)m(to)g(6)f(segmen)m
(ts.)69 b(The)0 3745 y(b)s(oundaries)38 b(b)s(et)m(w)m(een)h(cones)f
(are)f(simply)i(the)e(ra)m(ys)h(through)f(the)h Fs(x)2615
3760 y Fq(i)2644 3745 y Fu('s)f(and)g Fs(y)2988 3760
y Fq(i)3016 3745 y Fu('s.)58 b(Because)38 b(no)f(three)0
3861 y(p)s(oin)m(ts)27 b(of)f Fs(X)34 b Fu(or)27 b Fs(Y)47
b Fu(lie)27 b(in)g(the)g(same)h(half-circle,)g(eac)m(h)f(h)m(yp)s
(erplane)i(through)d FA(0)h Fu(and)f Fs(x)3219 3876 y
Fq(i)3274 3861 y Fu(divides)j(the)e Fs(y)3807 3876 y
Fq(i)3834 3861 y Fu('s)0 3977 y(2)35 b(to)g(1)g(and)g(vice-v)m(ersa.)54
b(Then)37 b(as)e(the)h(an)m(tip)s(o)s(de)f(of)g(a)g(p)s(oin)m(t)h(from)
f Fs(Z)42 b Fu(crosses)37 b Fs(x)3110 3992 y Fq(i)3174
3977 y Fu(or)e Fs(y)3344 3992 y Fq(i)3407 3977 y Fu(the)h(n)m(um)m(b)s
(er)0 4093 y(of)c(con)m(taining)h(simplicial)h(cones)g(c)m(hanges)g(b)m
(y)f(exactly)h(one.)100 4211 y(T)-8 b(o)22 b(get)h(a)g(con\014guration)
f FA(S)1100 4175 y Fj(\000)1182 4211 y Fu(where)i(only)f(5)g(simplices)
i(con)m(tain)e(0,)i(w)m(e)e(tak)m(e)h Fs(x)2958 4226
y Fo(1)3025 4211 y Fu(=)k(\()p Fn(\000)3244 4129 y(p)p
3327 4129 299 4 v 82 x Fu(1)22 b Fn(\000)h Fu(4)p Fs(\017)3586
4182 y Fo(2)3626 4211 y Fs(;)17 b Fn(\000)p Fu(2)p Fs(\017)p
Fu(\),)0 4334 y Fs(x)55 4349 y Fo(2)130 4334 y Fu(=)36
b(\()280 4252 y Fn(p)p 363 4252 250 4 v 82 x Fu(1)21
b Fn(\000)i Fs(\017)572 4305 y Fo(2)612 4334 y Fs(;)17
b(\017)p Fu(\),)38 b Fs(x)853 4349 y Fo(3)929 4334 y
Fu(=)d(\()p Fn(\000)p Fs(\017;)1238 4252 y Fn(p)p 1321
4252 V 82 x Fu(1)22 b Fn(\000)h Fs(\017)1531 4305 y Fo(2)1571
4334 y Fu(\),)38 b Fs(y)1722 4349 y Fo(1)1797 4334 y
Fu(=)d(\()1946 4252 y Fn(p)p 2029 4252 299 4 v 82 x Fu(1)22
b Fn(\000)g Fu(4)p Fs(\017)2287 4305 y Fo(2)2327 4334
y Fs(;)17 b Fn(\000)p Fu(2)p Fs(\017)p Fu(\),)39 b Fs(y)2688
4349 y Fo(2)2762 4334 y Fu(=)c(\()p Fn(\000)2988 4252
y(p)p 3072 4252 250 4 v 3072 4334 a Fu(1)22 b Fn(\000)g
Fs(\017)3281 4305 y Fo(2)3321 4334 y Fs(;)17 b(\017)p
Fu(\),)38 b(and)g Fs(y)3750 4349 y Fo(3)3824 4334 y Fu(=)0
4457 y(\()p Fs(\017;)121 4375 y Fn(p)p 204 4375 V 82
x Fu(1)22 b Fn(\000)h Fs(\017)414 4429 y Fo(2)453 4457
y Fu(\).)68 b(Observ)m(e)42 b(there)f(is)g(a)f(large)h(cell)g(of)f
(depth)h(1)g(b)s(et)m(w)m(een)h Fs(x)2780 4472 y Fo(1)2860
4457 y Fu(and)f Fs(y)3106 4472 y Fo(1)3145 4457 y Fu(.)67
b(The)42 b(reader)f(can)0 4574 y(v)m(erify)34 b(that)e(the)h(sequence)j
(of)c(colourful)g(cell)i(depths)g(is:)44 b(1,2,3,4,3,2.)832
5005 y @beginspecial 0 @llx 0 @lly 363 @urx 46 @ury 340
@rhi @setspecial
%%BeginDocument: circle.eps
%!PS-Adobe-2.0 EPSF-2.0
%%Title: circle.eps
%%Creator: fig2dev Version 3.2 Patchlevel 3c
%%CreationDate: Sat May  7 18:21:21 2005
%%For: tamon@birkhoff (Tamon Stephen,TTCA)
%%BoundingBox: 0 0 363 46
%%Magnification: 1.0000
%%EndComments
/$F2psDict 200 dict def
$F2psDict begin
$F2psDict /mtrx matrix put
/col-1 {0 setgray} bind def
/col0 {0.000 0.000 0.000 srgb} bind def
/col1 {0.000 0.000 1.000 srgb} bind def
/col2 {0.000 1.000 0.000 srgb} bind def
/col3 {0.000 1.000 1.000 srgb} bind def
/col4 {1.000 0.000 0.000 srgb} bind def
/col5 {1.000 0.000 1.000 srgb} bind def
/col6 {1.000 1.000 0.000 srgb} bind def
/col7 {1.000 1.000 1.000 srgb} bind def
/col8 {0.000 0.000 0.560 srgb} bind def
/col9 {0.000 0.000 0.690 srgb} bind def
/col10 {0.000 0.000 0.820 srgb} bind def
/col11 {0.530 0.810 1.000 srgb} bind def
/col12 {0.000 0.560 0.000 srgb} bind def
/col13 {0.000 0.690 0.000 srgb} bind def
/col14 {0.000 0.820 0.000 srgb} bind def
/col15 {0.000 0.560 0.560 srgb} bind def
/col16 {0.000 0.690 0.690 srgb} bind def
/col17 {0.000 0.820 0.820 srgb} bind def
/col18 {0.560 0.000 0.000 srgb} bind def
/col19 {0.690 0.000 0.000 srgb} bind def
/col20 {0.820 0.000 0.000 srgb} bind def
/col21 {0.560 0.000 0.560 srgb} bind def
/col22 {0.690 0.000 0.690 srgb} bind def
/col23 {0.820 0.000 0.820 srgb} bind def
/col24 {0.500 0.190 0.000 srgb} bind def
/col25 {0.630 0.250 0.000 srgb} bind def
/col26 {0.750 0.380 0.000 srgb} bind def
/col27 {1.000 0.500 0.500 srgb} bind def
/col28 {1.000 0.630 0.630 srgb} bind def
/col29 {1.000 0.750 0.750 srgb} bind def
/col30 {1.000 0.880 0.880 srgb} bind def
/col31 {1.000 0.840 0.000 srgb} bind def

end
save
newpath 0 46 moveto 0 0 lineto 363 0 lineto 363 46 lineto closepath clip newpath
-66.0 99.0 translate
1 -1 scale

/cp {closepath} bind def
/ef {eofill} bind def
/gr {grestore} bind def
/gs {gsave} bind def
/sa {save} bind def
/rs {restore} bind def
/l {lineto} bind def
/m {moveto} bind def
/rm {rmoveto} bind def
/n {newpath} bind def
/s {stroke} bind def
/sh {show} bind def
/slc {setlinecap} bind def
/slj {setlinejoin} bind def
/slw {setlinewidth} bind def
/srgb {setrgbcolor} bind def
/rot {rotate} bind def
/sc {scale} bind def
/sd {setdash} bind def
/ff {findfont} bind def
/sf {setfont} bind def
/scf {scalefont} bind def
/sw {stringwidth} bind def
/tr {translate} bind def
/tnt {dup dup currentrgbcolor
  4 -2 roll dup 1 exch sub 3 -1 roll mul add
  4 -2 roll dup 1 exch sub 3 -1 roll mul add
  4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb}
  bind def
/shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul
  4 -2 roll mul srgb} bind def
 /DrawEllipse {
	/endangle exch def
	/startangle exch def
	/yrad exch def
	/xrad exch def
	/y exch def
	/x exch def
	/savematrix mtrx currentmatrix def
	x y tr xrad yrad sc 0 0 1 startangle endangle arc
	closepath
	savematrix setmatrix
	} def

/$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def
/$F2psEnd {$F2psEnteredState restore end} def

$F2psBegin
%%Page: 1 1
10 setmiterlimit
 0.06000 0.06000 sc
%
% Fig objects follow
%
% Polyline
7.500 slw
n 1150 1150 m
 1150 1225 l gs col0 s gr 
% Polyline
n 1175 1150 m
 1175 1225 l gs col0 s gr 
% Polyline
n 7075 1150 m
 7075 1225 l gs col0 s gr 
% Polyline
n 7100 1150 m
 7100 1225 l gs col0 s gr 
/Times-BoldItalic ff 300.00 scf sf
1800 1575 m
gs 1 -1 sc (x) col0 sh gr
/Times-Italic ff 180.00 scf sf
1950 1650 m
gs 1 -1 sc (1) col0 sh gr
/Times-BoldItalic ff 300.00 scf sf
2550 1575 m
gs 1 -1 sc (y) col0 sh gr
/Times-Italic ff 180.00 scf sf
2700 1650 m
gs 1 -1 sc (2) col0 sh gr
/Times-BoldItalic ff 300.00 scf sf
3450 1575 m
gs 1 -1 sc (x) col0 sh gr
/Times-Italic ff 180.00 scf sf
3600 1650 m
gs 1 -1 sc (3) col0 sh gr
/Times-BoldItalic ff 300.00 scf sf
4425 1575 m
gs 1 -1 sc (y) col0 sh gr
/Times-Italic ff 180.00 scf sf
4575 1650 m
gs 1 -1 sc (3) col0 sh gr
/Times-BoldItalic ff 300.00 scf sf
5550 1575 m
gs 1 -1 sc (x) col0 sh gr
/Times-Italic ff 180.00 scf sf
5700 1650 m
gs 1 -1 sc (2) col0 sh gr
/Times-BoldItalic ff 300.00 scf sf
6450 1575 m
gs 1 -1 sc (y) col0 sh gr
/Times-Italic ff 180.00 scf sf
6600 1650 m
gs 1 -1 sc (1) col0 sh gr
15.000 slw
% Ellipse
n 1800 1200 38 38 0 360 DrawEllipse gs col0 s gr

% Ellipse
n 6600 1200 38 38 0 360 DrawEllipse gs col0 s gr

% Ellipse
n 2700 1200 38 38 0 360 DrawEllipse gs col0 s gr

% Ellipse
n 3600 1200 38 38 0 360 DrawEllipse gs col0 s gr

% Ellipse
n 4575 1200 38 38 0 360 DrawEllipse gs col0 s gr

% Ellipse
n 5700 1200 38 38 0 360 DrawEllipse gs col0 s gr

% Polyline
n 1125 1200 m
 7125 1200 l gs col0 s gr 
/Times-Roman ff 240.00 scf sf
2175 1050 m
gs 1 -1 sc (2) col0 sh gr
/Times-Roman ff 240.00 scf sf
3150 1050 m
gs 1 -1 sc (3) col0 sh gr
/Times-Roman ff 240.00 scf sf
4050 1050 m
gs 1 -1 sc (4) col0 sh gr
/Times-Roman ff 240.00 scf sf
5025 1050 m
gs 1 -1 sc (3) col0 sh gr
/Times-Roman ff 240.00 scf sf
6075 1050 m
gs 1 -1 sc (2) col0 sh gr
/Times-Roman ff 240.00 scf sf
6900 1050 m
gs 1 -1 sc (1) col0 sh gr
/Times-Roman ff 240.00 scf sf
1350 1050 m
gs 1 -1 sc (1) col0 sh gr
$F2psEnd
rs

%%EndDocument
 @endspecial 673 5221 a Ft(Figure)38 b(3.)48 b Fu(Co)m(v)m(ering)35
b(depths)e(for)f(a)h(circle)g(with)h(a)e(depth)h(1)g(cell.)p
eop end
%%Page: 13 13
TeXDict begin 13 12 bop 1304 71 a Fl(COLOURFUL)32 b(SIMPLICIAL)g(DEPTH)
1227 b(13)100 281 y Fu(Let)41 b Fs(Z)49 b Fu(=)42 b Fn(f)p
Fs(z)612 296 y Fo(1)652 281 y Fs(;)17 b(z)741 296 y Fo(2)780
281 y Fs(;)g(z)869 296 y Fo(3)909 281 y Fn(g)p Fu(.)69
b(Place)42 b Fs(z)1370 296 y Fo(2)1452 281 y Fu(=)g(\()p
Fn(\000)1685 199 y(p)p 1769 199 299 4 v 1769 281 a Fu(1)22
b Fn(\000)g Fu(9)p Fs(\017)2027 252 y Fo(2)2067 281 y
Fs(;)17 b Fu(3)p Fs(\017)p Fu(\))41 b(and)g Fs(z)2521
296 y Fo(3)2603 281 y Fu(=)h(\()2759 199 y Fn(p)p 2842
199 V 82 x Fu(1)22 b Fn(\000)h Fu(9)p Fs(\017)3101 252
y Fo(2)3140 281 y Fs(;)17 b Fu(3)p Fs(\017)p Fu(\))41
b(so)h(that)e(their)0 397 y(an)m(tip)s(o)s(des)j(lie)f(b)s(et)m(w)m
(een)i Fs(x)1032 412 y Fo(1)1114 397 y Fu(and)e Fs(y)1361
412 y Fo(1)1400 397 y Fu(.)72 b(They)44 b(eac)m(h)f(generate)g(one)f
(simplex)i(con)m(taining)f FA(0)p Fu(.)72 b(Finally)-8
b(,)0 513 y(to)51 b(ensure)j(that)d FA(0)60 b Fn(2)h
Fu(con)m(v)r(\()p Fs(Z)7 b Fu(\),)57 b(w)m(e)52 b(see)h(that)f
Fn(\000)p Fs(z)2057 528 y Fo(1)2149 513 y Fu(m)m(ust)g(lie)h(ab)s(o)m
(v)m(e)f Fs(y)2902 528 y Fo(2)2993 513 y Fu(and)g Fs(x)3257
528 y Fo(2)3296 513 y Fu(.)101 b(T)-8 b(ak)m(e)53 b Fs(z)3724
528 y Fo(1)3824 513 y Fu(=)0 636 y(\()p Fn(\000)115 554
y(p)p 198 554 347 4 v 82 x Fu(1)22 b Fn(\000)h Fu(16)p
Fs(\017)506 608 y Fo(2)545 636 y Fs(;)17 b Fn(\000)p
Fu(4)p Fs(\017)p Fu(\).)62 b(Then)40 b Fn(\000)p Fs(z)1264
651 y Fo(1)1343 636 y Fu(is)f(con)m(tained)h(in)f(3)f(colourful)h
(simplicial)h(cones)g(generated)g(b)m(y)f Fs(X)0 753
y Fu(and)28 b Fs(Y)21 b Fu(.)42 b(This)28 b(con\014guration)g(has)g
FA(0)f Fu(in)h(the)g(in)m(terior)g(of)f(its)h(core)g(and)f
FA(0)h Fu(lies)g(in)g(1)12 b(+)g(1)g(+)g(3)26 b(=)i(5)f(colourful)0
869 y(simplices.)572 2198 y @beginspecial 0 @llx 0 @lly
406 @urx 174 @ury 1417 @rhi @setspecial
%%BeginDocument: min2d.eps
%!PS-Adobe-2.0 EPSF-2.0
%%Title: min2d.eps
%%Creator: fig2dev Version 3.2 Patchlevel 3c
%%CreationDate: Fri May 27 15:26:29 2005
%%For: tamon@birkhoff (Tamon Stephen,TTCA)
%%BoundingBox: 0 0 406 174
%%Magnification: 1.0000
%%EndComments
/$F2psDict 200 dict def
$F2psDict begin
$F2psDict /mtrx matrix put
/col-1 {0 setgray} bind def
/col0 {0.000 0.000 0.000 srgb} bind def
/col1 {0.000 0.000 1.000 srgb} bind def
/col2 {0.000 1.000 0.000 srgb} bind def
/col3 {0.000 1.000 1.000 srgb} bind def
/col4 {1.000 0.000 0.000 srgb} bind def
/col5 {1.000 0.000 1.000 srgb} bind def
/col6 {1.000 1.000 0.000 srgb} bind def
/col7 {1.000 1.000 1.000 srgb} bind def
/col8 {0.000 0.000 0.560 srgb} bind def
/col9 {0.000 0.000 0.690 srgb} bind def
/col10 {0.000 0.000 0.820 srgb} bind def
/col11 {0.530 0.810 1.000 srgb} bind def
/col12 {0.000 0.560 0.000 srgb} bind def
/col13 {0.000 0.690 0.000 srgb} bind def
/col14 {0.000 0.820 0.000 srgb} bind def
/col15 {0.000 0.560 0.560 srgb} bind def
/col16 {0.000 0.690 0.690 srgb} bind def
/col17 {0.000 0.820 0.820 srgb} bind def
/col18 {0.560 0.000 0.000 srgb} bind def
/col19 {0.690 0.000 0.000 srgb} bind def
/col20 {0.820 0.000 0.000 srgb} bind def
/col21 {0.560 0.000 0.560 srgb} bind def
/col22 {0.690 0.000 0.690 srgb} bind def
/col23 {0.820 0.000 0.820 srgb} bind def
/col24 {0.500 0.190 0.000 srgb} bind def
/col25 {0.630 0.250 0.000 srgb} bind def
/col26 {0.750 0.380 0.000 srgb} bind def
/col27 {1.000 0.500 0.500 srgb} bind def
/col28 {1.000 0.630 0.630 srgb} bind def
/col29 {1.000 0.750 0.750 srgb} bind def
/col30 {1.000 0.880 0.880 srgb} bind def
/col31 {1.000 0.840 0.000 srgb} bind def
/col32 {0.412 0.427 0.412 srgb} bind def
/col33 {0.525 0.510 0.525 srgb} bind def
/col34 {0.745 0.765 0.745 srgb} bind def
/col35 {0.875 0.890 0.875 srgb} bind def
/col36 {0.525 0.510 0.525 srgb} bind def
/col37 {0.745 0.765 0.745 srgb} bind def
/col38 {0.875 0.890 0.875 srgb} bind def
/col39 {0.286 0.271 0.286 srgb} bind def
/col40 {0.286 0.271 0.286 srgb} bind def
/col41 {0.557 0.557 0.557 srgb} bind def
/col42 {0.620 0.000 0.000 srgb} bind def
/col43 {0.620 0.000 0.000 srgb} bind def
/col44 {0.557 0.557 0.557 srgb} bind def
/col45 {0.255 0.255 0.255 srgb} bind def
/col46 {0.557 0.557 0.557 srgb} bind def
/col47 {0.255 0.255 0.255 srgb} bind def
/col48 {0.557 0.557 0.557 srgb} bind def
/col49 {0.255 0.255 0.255 srgb} bind def
/col50 {0.557 0.557 0.557 srgb} bind def
/col51 {0.255 0.255 0.255 srgb} bind def
/col52 {0.557 0.557 0.557 srgb} bind def
/col53 {0.255 0.255 0.255 srgb} bind def
/col54 {0.557 0.557 0.557 srgb} bind def
/col55 {0.255 0.255 0.255 srgb} bind def
/col56 {0.557 0.557 0.557 srgb} bind def
/col57 {0.255 0.255 0.255 srgb} bind def
/col58 {0.557 0.557 0.557 srgb} bind def
/col59 {0.255 0.255 0.255 srgb} bind def
/col60 {0.557 0.557 0.557 srgb} bind def
/col61 {0.255 0.255 0.255 srgb} bind def
/col62 {0.557 0.557 0.557 srgb} bind def
/col63 {0.255 0.255 0.255 srgb} bind def
/col64 {0.557 0.557 0.557 srgb} bind def
/col65 {0.255 0.255 0.255 srgb} bind def
/col66 {0.557 0.557 0.557 srgb} bind def
/col67 {0.255 0.255 0.255 srgb} bind def
/col68 {0.557 0.557 0.557 srgb} bind def
/col69 {0.255 0.255 0.255 srgb} bind def
/col70 {0.557 0.557 0.557 srgb} bind def
/col71 {0.255 0.255 0.255 srgb} bind def
/col72 {0.557 0.557 0.557 srgb} bind def
/col73 {0.255 0.255 0.255 srgb} bind def
/col74 {0.557 0.557 0.557 srgb} bind def
/col75 {0.255 0.255 0.255 srgb} bind def
/col76 {0.557 0.557 0.557 srgb} bind def
/col77 {0.255 0.255 0.255 srgb} bind def
/col78 {0.557 0.557 0.557 srgb} bind def
/col79 {0.255 0.255 0.255 srgb} bind def
/col80 {0.745 0.765 0.745 srgb} bind def
/col81 {0.412 0.427 0.412 srgb} bind def
/col82 {0.745 0.765 0.745 srgb} bind def
/col83 {0.412 0.427 0.412 srgb} bind def
/col84 {0.286 0.271 0.286 srgb} bind def
/col85 {0.557 0.557 0.557 srgb} bind def
/col86 {0.412 0.427 0.412 srgb} bind def
/col87 {0.557 0.557 0.557 srgb} bind def
/col88 {0.443 0.443 0.443 srgb} bind def
/col89 {0.682 0.682 0.682 srgb} bind def
/col90 {0.188 0.188 0.188 srgb} bind def
/col91 {0.588 0.573 0.588 srgb} bind def
/col92 {0.443 0.443 0.443 srgb} bind def
/col93 {0.349 0.333 0.349 srgb} bind def
/col94 {0.682 0.698 0.682 srgb} bind def
/col95 {0.745 0.765 0.745 srgb} bind def
/col96 {0.286 0.271 0.286 srgb} bind def
/col97 {0.412 0.427 0.412 srgb} bind def
/col98 {0.286 0.271 0.286 srgb} bind def
/col99 {0.412 0.427 0.412 srgb} bind def
/col100 {0.745 0.765 0.745 srgb} bind def
/col101 {0.412 0.427 0.412 srgb} bind def
/col102 {0.286 0.271 0.286 srgb} bind def
/col103 {0.745 0.765 0.745 srgb} bind def
/col104 {0.412 0.427 0.412 srgb} bind def
/col105 {0.745 0.765 0.745 srgb} bind def
/col106 {0.286 0.271 0.286 srgb} bind def
/col107 {0.557 0.557 0.557 srgb} bind def
/col108 {0.875 0.890 0.937 srgb} bind def
/col109 {0.588 0.588 0.620 srgb} bind def
/col110 {0.843 0.859 0.843 srgb} bind def
/col111 {0.620 0.635 0.714 srgb} bind def
/col112 {0.620 0.000 0.000 srgb} bind def
/col113 {0.937 0.937 0.937 srgb} bind def
/col114 {0.875 0.890 0.875 srgb} bind def
/col115 {0.525 0.682 1.000 srgb} bind def
/col116 {0.443 0.443 1.000 srgb} bind def
/col117 {0.620 0.000 0.000 srgb} bind def
/col118 {0.620 0.000 0.000 srgb} bind def
/col119 {0.557 0.557 0.557 srgb} bind def
/col120 {0.255 0.255 0.255 srgb} bind def
/col121 {0.557 0.557 0.557 srgb} bind def
/col122 {0.255 0.255 0.255 srgb} bind def
/col123 {0.557 0.557 0.557 srgb} bind def
/col124 {0.255 0.255 0.255 srgb} bind def
/col125 {0.557 0.557 0.557 srgb} bind def
/col126 {0.255 0.255 0.255 srgb} bind def
/col127 {0.557 0.557 0.557 srgb} bind def
/col128 {0.255 0.255 0.255 srgb} bind def
/col129 {0.557 0.557 0.557 srgb} bind def
/col130 {0.255 0.255 0.255 srgb} bind def
/col131 {0.557 0.557 0.557 srgb} bind def
/col132 {0.255 0.255 0.255 srgb} bind def
/col133 {0.557 0.557 0.557 srgb} bind def
/col134 {0.255 0.255 0.255 srgb} bind def
/col135 {0.557 0.557 0.557 srgb} bind def
/col136 {0.255 0.255 0.255 srgb} bind def
/col137 {0.557 0.557 0.557 srgb} bind def
/col138 {0.255 0.255 0.255 srgb} bind def
/col139 {0.557 0.557 0.557 srgb} bind def
/col140 {0.255 0.255 0.255 srgb} bind def
/col141 {0.557 0.557 0.557 srgb} bind def
/col142 {0.255 0.255 0.255 srgb} bind def
/col143 {0.557 0.557 0.557 srgb} bind def
/col144 {0.255 0.255 0.255 srgb} bind def
/col145 {0.557 0.557 0.557 srgb} bind def
/col146 {0.255 0.255 0.255 srgb} bind def
/col147 {0.557 0.557 0.557 srgb} bind def
/col148 {0.255 0.255 0.255 srgb} bind def
/col149 {0.557 0.557 0.557 srgb} bind def
/col150 {0.255 0.255 0.255 srgb} bind def
/col151 {0.557 0.557 0.557 srgb} bind def
/col152 {0.255 0.255 0.255 srgb} bind def
/col153 {0.557 0.557 0.557 srgb} bind def
/col154 {0.255 0.255 0.255 srgb} bind def
/col155 {0.745 0.765 0.745 srgb} bind def
/col156 {0.412 0.427 0.412 srgb} bind def
/col157 {0.745 0.765 0.745 srgb} bind def
/col158 {0.412 0.427 0.412 srgb} bind def
/col159 {0.286 0.271 0.286 srgb} bind def
/col160 {0.557 0.557 0.557 srgb} bind def
/col161 {0.412 0.427 0.412 srgb} bind def
/col162 {0.557 0.557 0.557 srgb} bind def
/col163 {0.188 0.188 0.188 srgb} bind def
/col164 {0.588 0.573 0.588 srgb} bind def
/col165 {0.443 0.443 0.443 srgb} bind def
/col166 {0.349 0.333 0.349 srgb} bind def
/col167 {0.682 0.698 0.682 srgb} bind def
/col168 {0.745 0.765 0.745 srgb} bind def
/col169 {0.286 0.271 0.286 srgb} bind def
/col170 {0.412 0.427 0.412 srgb} bind def
/col171 {0.286 0.271 0.286 srgb} bind def
/col172 {0.412 0.427 0.412 srgb} bind def
/col173 {0.745 0.765 0.745 srgb} bind def
/col174 {0.412 0.427 0.412 srgb} bind def
/col175 {0.286 0.271 0.286 srgb} bind def
/col176 {0.745 0.765 0.745 srgb} bind def
/col177 {0.412 0.427 0.412 srgb} bind def
/col178 {0.745 0.765 0.745 srgb} bind def
/col179 {0.286 0.271 0.286 srgb} bind def
/col180 {0.557 0.557 0.557 srgb} bind def
/col181 {0.875 0.620 0.557 srgb} bind def
/col182 {0.937 0.937 0.875 srgb} bind def
/col183 {0.745 0.765 0.745 srgb} bind def
/col184 {0.875 0.796 0.682 srgb} bind def
/col185 {0.875 0.890 0.875 srgb} bind def
/col186 {0.812 0.827 0.812 srgb} bind def
/col187 {0.937 0.937 0.937 srgb} bind def
/col188 {0.843 0.475 0.094 srgb} bind def
/col189 {0.937 0.906 0.094 srgb} bind def
/col190 {0.557 0.490 0.745 srgb} bind def
/col191 {0.843 0.843 0.843 srgb} bind def
/col192 {0.557 0.557 0.651 srgb} bind def
/col193 {0.286 0.286 0.286 srgb} bind def
/col194 {0.557 0.412 0.412 srgb} bind def
/col195 {0.349 0.349 0.349 srgb} bind def
/col196 {0.380 0.380 0.380 srgb} bind def
/col197 {0.714 0.604 0.443 srgb} bind def
/col198 {0.255 0.573 1.000 srgb} bind def
/col199 {0.745 0.443 0.220 srgb} bind def
/col200 {0.843 0.459 0.000 srgb} bind def
/col201 {0.843 0.729 0.000 srgb} bind def
/col202 {0.000 0.396 0.000 srgb} bind def
/col203 {0.349 0.412 0.220 srgb} bind def
/col204 {0.812 0.827 0.812 srgb} bind def
/col205 {0.682 0.667 0.682 srgb} bind def
/col206 {0.557 0.557 0.651 srgb} bind def
/col207 {0.937 0.729 0.349 srgb} bind def
/col208 {0.557 0.604 0.412 srgb} bind def
/col209 {0.286 0.286 0.286 srgb} bind def
/col210 {0.380 0.396 0.380 srgb} bind def
/col211 {0.843 0.843 0.843 srgb} bind def
/col212 {0.557 0.557 0.651 srgb} bind def
/col213 {0.349 0.349 0.349 srgb} bind def
/col214 {0.380 0.380 0.380 srgb} bind def
/col215 {0.714 0.906 1.000 srgb} bind def
/col216 {0.525 0.765 0.937 srgb} bind def
/col217 {0.745 0.745 0.745 srgb} bind def
/col218 {0.812 0.588 0.318 srgb} bind def
/col219 {0.620 0.827 1.000 srgb} bind def
/col220 {0.843 0.843 0.843 srgb} bind def
/col221 {0.557 0.557 0.651 srgb} bind def
/col222 {0.557 0.412 0.412 srgb} bind def
/col223 {0.349 0.349 0.349 srgb} bind def
/col224 {0.380 0.380 0.380 srgb} bind def
/col225 {0.557 0.620 0.412 srgb} bind def
/col226 {0.969 0.412 0.000 srgb} bind def
/col227 {0.349 0.412 0.220 srgb} bind def
/col228 {0.557 0.620 0.412 srgb} bind def
/col229 {0.286 0.286 0.286 srgb} bind def
/col230 {0.843 0.843 0.843 srgb} bind def
/col231 {0.557 0.557 0.651 srgb} bind def
/col232 {0.557 0.412 0.412 srgb} bind def
/col233 {0.349 0.349 0.349 srgb} bind def
/col234 {0.380 0.380 0.380 srgb} bind def
/col235 {0.557 0.620 0.412 srgb} bind def
/col236 {0.969 0.412 0.000 srgb} bind def
/col237 {0.557 0.620 0.475 srgb} bind def
/col238 {0.286 0.286 0.286 srgb} bind def
/col239 {0.094 0.286 0.094 srgb} bind def
/col240 {0.349 0.412 0.220 srgb} bind def
/col241 {0.843 0.843 0.843 srgb} bind def
/col242 {0.682 0.682 0.682 srgb} bind def
/col243 {0.557 0.557 0.651 srgb} bind def
/col244 {0.969 0.745 0.349 srgb} bind def
/col245 {0.557 0.620 0.412 srgb} bind def
/col246 {0.286 0.286 0.286 srgb} bind def
/col247 {0.380 0.380 0.380 srgb} bind def
/col248 {0.380 0.412 0.620 srgb} bind def
/col249 {0.557 0.412 0.412 srgb} bind def
/col250 {0.969 0.969 0.969 srgb} bind def
/col251 {0.875 0.000 0.000 srgb} bind def
/col252 {0.349 0.349 0.349 srgb} bind def
/col253 {0.557 0.620 0.412 srgb} bind def
/col254 {0.286 0.286 0.286 srgb} bind def
/col255 {0.380 0.380 0.380 srgb} bind def
/col256 {0.349 0.412 0.220 srgb} bind def
/col257 {0.843 0.843 0.843 srgb} bind def
/col258 {0.682 0.682 0.682 srgb} bind def
/col259 {0.557 0.557 0.651 srgb} bind def
/col260 {0.969 0.745 0.349 srgb} bind def
/col261 {0.557 0.620 0.412 srgb} bind def
/col262 {0.286 0.286 0.286 srgb} bind def
/col263 {0.380 0.380 0.380 srgb} bind def
/col264 {0.349 0.412 0.220 srgb} bind def
/col265 {0.843 0.843 0.843 srgb} bind def
/col266 {0.682 0.682 0.682 srgb} bind def
/col267 {0.557 0.557 0.651 srgb} bind def
/col268 {0.969 0.745 0.349 srgb} bind def
/col269 {0.557 0.620 0.412 srgb} bind def
/col270 {0.286 0.286 0.286 srgb} bind def
/col271 {0.380 0.380 0.380 srgb} bind def
/col272 {0.380 0.412 0.620 srgb} bind def
/col273 {0.318 0.412 0.157 srgb} bind def
/col274 {0.380 0.380 0.380 srgb} bind def
/col275 {0.349 0.412 0.220 srgb} bind def
/col276 {0.588 0.588 0.588 srgb} bind def
/col277 {0.380 0.380 0.380 srgb} bind def
/col278 {0.000 0.380 0.000 srgb} bind def
/col279 {0.557 0.557 0.651 srgb} bind def
/col280 {0.557 0.557 0.651 srgb} bind def
/col281 {0.557 0.557 0.651 srgb} bind def
/col282 {0.000 0.380 0.286 srgb} bind def
/col283 {0.475 0.525 0.286 srgb} bind def
/col284 {0.906 0.745 0.475 srgb} bind def
/col285 {0.557 0.620 0.475 srgb} bind def
/col286 {0.651 0.714 0.780 srgb} bind def
/col287 {0.412 0.412 0.588 srgb} bind def
/col288 {0.525 0.412 0.412 srgb} bind def
/col289 {0.318 0.620 0.286 srgb} bind def
/col290 {0.843 0.906 0.906 srgb} bind def
/col291 {0.318 0.380 0.380 srgb} bind def
/col292 {0.094 0.412 0.286 srgb} bind def
/col293 {0.620 0.651 0.714 srgb} bind def
/col294 {1.000 0.588 0.000 srgb} bind def
/col295 {1.000 0.588 0.000 srgb} bind def
/col296 {0.557 0.412 0.412 srgb} bind def
/col297 {0.000 0.380 0.286 srgb} bind def
/col298 {0.475 0.525 0.286 srgb} bind def
/col299 {0.380 0.443 0.475 srgb} bind def
/col300 {0.906 0.745 0.475 srgb} bind def
/col301 {0.094 0.286 0.094 srgb} bind def
/col302 {0.349 0.412 0.220 srgb} bind def
/col303 {0.557 0.557 0.651 srgb} bind def
/col304 {0.969 0.745 0.349 srgb} bind def
/col305 {0.557 0.620 0.412 srgb} bind def
/col306 {0.286 0.286 0.286 srgb} bind def
/col307 {0.380 0.380 0.380 srgb} bind def
/col308 {0.843 0.843 0.843 srgb} bind def
/col309 {0.682 0.682 0.682 srgb} bind def
/col310 {0.557 0.557 0.651 srgb} bind def
/col311 {0.286 0.286 0.286 srgb} bind def
/col312 {0.380 0.380 0.380 srgb} bind def
/col313 {0.557 0.412 0.412 srgb} bind def
/col314 {0.349 0.349 0.349 srgb} bind def
/col315 {0.286 0.286 0.286 srgb} bind def
/col316 {0.380 0.380 0.380 srgb} bind def
/col317 {0.682 0.682 0.682 srgb} bind def
/col318 {0.380 0.380 0.380 srgb} bind def
/col319 {0.557 0.620 0.412 srgb} bind def
/col320 {0.286 0.286 0.286 srgb} bind def
/col321 {0.349 0.412 0.220 srgb} bind def
/col322 {0.682 0.682 0.682 srgb} bind def
/col323 {0.286 0.286 0.286 srgb} bind def
/col324 {0.000 0.396 0.000 srgb} bind def
/col325 {0.349 0.412 0.220 srgb} bind def
/col326 {0.812 0.827 0.812 srgb} bind def
/col327 {0.682 0.667 0.682 srgb} bind def
/col328 {0.557 0.557 0.651 srgb} bind def
/col329 {0.937 0.729 0.349 srgb} bind def
/col330 {0.557 0.604 0.412 srgb} bind def
/col331 {0.286 0.286 0.286 srgb} bind def
/col332 {0.380 0.396 0.380 srgb} bind def
/col333 {0.843 0.843 0.843 srgb} bind def
/col334 {0.557 0.557 0.651 srgb} bind def
/col335 {0.349 0.349 0.349 srgb} bind def
/col336 {0.380 0.380 0.380 srgb} bind def
/col337 {0.843 0.843 0.843 srgb} bind def
/col338 {0.349 0.412 0.220 srgb} bind def
/col339 {0.557 0.557 0.651 srgb} bind def
/col340 {0.557 0.412 0.412 srgb} bind def
/col341 {0.349 0.349 0.349 srgb} bind def
/col342 {0.380 0.380 0.380 srgb} bind def
/col343 {0.557 0.620 0.412 srgb} bind def
/col344 {0.286 0.286 0.286 srgb} bind def
/col345 {0.843 0.843 0.843 srgb} bind def
/col346 {0.557 0.557 0.651 srgb} bind def
/col347 {0.557 0.412 0.412 srgb} bind def
/col348 {0.349 0.349 0.349 srgb} bind def
/col349 {0.380 0.380 0.380 srgb} bind def
/col350 {0.557 0.620 0.475 srgb} bind def
/col351 {0.286 0.286 0.286 srgb} bind def
/col352 {0.000 0.380 0.000 srgb} bind def
/col353 {0.349 0.412 0.220 srgb} bind def
/col354 {0.875 0.875 0.875 srgb} bind def
/col355 {0.682 0.682 0.682 srgb} bind def
/col356 {0.557 0.557 0.651 srgb} bind def
/col357 {0.969 0.745 0.349 srgb} bind def
/col358 {0.557 0.620 0.412 srgb} bind def
/col359 {0.286 0.286 0.286 srgb} bind def
/col360 {0.380 0.380 0.380 srgb} bind def
/col361 {0.380 0.412 0.620 srgb} bind def
/col362 {0.843 0.843 0.843 srgb} bind def
/col363 {0.557 0.412 0.412 srgb} bind def
/col364 {0.349 0.349 0.349 srgb} bind def
/col365 {0.000 0.396 0.000 srgb} bind def
/col366 {0.349 0.412 0.220 srgb} bind def
/col367 {0.812 0.827 0.812 srgb} bind def
/col368 {0.682 0.667 0.682 srgb} bind def
/col369 {0.557 0.557 0.651 srgb} bind def
/col370 {0.937 0.729 0.349 srgb} bind def
/col371 {0.557 0.604 0.412 srgb} bind def
/col372 {0.286 0.286 0.286 srgb} bind def
/col373 {0.380 0.396 0.380 srgb} bind def
/col374 {0.349 0.412 0.220 srgb} bind def
/col375 {0.812 0.827 0.812 srgb} bind def
/col376 {0.682 0.667 0.682 srgb} bind def
/col377 {0.557 0.557 0.651 srgb} bind def
/col378 {0.937 0.729 0.349 srgb} bind def
/col379 {0.557 0.604 0.412 srgb} bind def
/col380 {0.286 0.286 0.286 srgb} bind def
/col381 {0.380 0.396 0.380 srgb} bind def
/col382 {0.349 0.412 0.220 srgb} bind def
/col383 {0.812 0.827 0.812 srgb} bind def
/col384 {0.682 0.667 0.682 srgb} bind def
/col385 {0.557 0.557 0.651 srgb} bind def
/col386 {0.937 0.729 0.349 srgb} bind def
/col387 {0.557 0.604 0.412 srgb} bind def
/col388 {0.286 0.286 0.286 srgb} bind def
/col389 {0.380 0.396 0.380 srgb} bind def
/col390 {0.349 0.412 0.220 srgb} bind def
/col391 {0.812 0.827 0.812 srgb} bind def
/col392 {0.682 0.667 0.682 srgb} bind def
/col393 {0.557 0.557 0.651 srgb} bind def
/col394 {0.937 0.729 0.349 srgb} bind def
/col395 {0.557 0.604 0.412 srgb} bind def
/col396 {0.286 0.286 0.286 srgb} bind def
/col397 {0.380 0.396 0.380 srgb} bind def
/col398 {0.349 0.412 0.220 srgb} bind def
/col399 {0.812 0.827 0.812 srgb} bind def
/col400 {0.682 0.667 0.682 srgb} bind def
/col401 {0.557 0.557 0.651 srgb} bind def
/col402 {0.937 0.729 0.349 srgb} bind def
/col403 {0.557 0.604 0.412 srgb} bind def
/col404 {0.286 0.286 0.286 srgb} bind def
/col405 {0.380 0.396 0.380 srgb} bind def
/col406 {0.843 0.843 0.843 srgb} bind def
/col407 {0.557 0.557 0.651 srgb} bind def
/col408 {0.349 0.349 0.349 srgb} bind def
/col409 {0.380 0.380 0.380 srgb} bind def
/col410 {0.000 0.396 0.000 srgb} bind def
/col411 {0.349 0.412 0.220 srgb} bind def
/col412 {0.812 0.827 0.812 srgb} bind def
/col413 {0.682 0.667 0.682 srgb} bind def
/col414 {0.557 0.557 0.651 srgb} bind def
/col415 {0.937 0.729 0.349 srgb} bind def
/col416 {0.557 0.604 0.412 srgb} bind def
/col417 {0.286 0.286 0.286 srgb} bind def
/col418 {0.380 0.396 0.380 srgb} bind def
/col419 {0.349 0.412 0.220 srgb} bind def
/col420 {0.812 0.827 0.812 srgb} bind def
/col421 {0.682 0.667 0.682 srgb} bind def
/col422 {0.557 0.557 0.651 srgb} bind def
/col423 {0.937 0.729 0.349 srgb} bind def
/col424 {0.557 0.604 0.412 srgb} bind def
/col425 {0.286 0.286 0.286 srgb} bind def
/col426 {0.380 0.396 0.380 srgb} bind def
/col427 {0.349 0.412 0.220 srgb} bind def
/col428 {0.812 0.827 0.812 srgb} bind def
/col429 {0.682 0.667 0.682 srgb} bind def
/col430 {0.557 0.557 0.651 srgb} bind def
/col431 {0.937 0.729 0.349 srgb} bind def
/col432 {0.557 0.604 0.412 srgb} bind def
/col433 {0.286 0.286 0.286 srgb} bind def
/col434 {0.380 0.396 0.380 srgb} bind def
/col435 {0.349 0.412 0.220 srgb} bind def
/col436 {0.812 0.827 0.812 srgb} bind def
/col437 {0.682 0.667 0.682 srgb} bind def
/col438 {0.557 0.557 0.651 srgb} bind def
/col439 {0.937 0.729 0.349 srgb} bind def
/col440 {0.557 0.604 0.412 srgb} bind def
/col441 {0.286 0.286 0.286 srgb} bind def
/col442 {0.380 0.396 0.380 srgb} bind def
/col443 {0.843 0.843 0.843 srgb} bind def
/col444 {0.557 0.557 0.651 srgb} bind def
/col445 {0.349 0.349 0.349 srgb} bind def
/col446 {0.380 0.380 0.380 srgb} bind def
/col447 {0.937 0.937 0.812 srgb} bind def
/col448 {0.969 0.682 0.349 srgb} bind def
/col449 {0.588 0.812 0.620 srgb} bind def
/col450 {0.682 0.667 0.682 srgb} bind def
/col451 {0.714 0.078 0.475 srgb} bind def
/col452 {0.937 0.937 0.937 srgb} bind def
/col453 {0.525 0.525 0.525 srgb} bind def
/col454 {0.000 0.380 0.000 srgb} bind def
/col455 {0.349 0.412 0.220 srgb} bind def
/col456 {0.843 0.843 0.843 srgb} bind def
/col457 {0.682 0.682 0.682 srgb} bind def
/col458 {0.557 0.557 0.651 srgb} bind def
/col459 {0.969 0.745 0.349 srgb} bind def
/col460 {0.557 0.620 0.412 srgb} bind def
/col461 {0.286 0.286 0.286 srgb} bind def
/col462 {0.380 0.380 0.380 srgb} bind def
/col463 {0.380 0.412 0.620 srgb} bind def
/col464 {0.475 0.475 0.475 srgb} bind def
/col465 {0.000 0.349 0.000 srgb} bind def
/col466 {0.906 0.443 0.443 srgb} bind def
/col467 {0.875 0.000 0.000 srgb} bind def
/col468 {1.000 0.796 0.188 srgb} bind def
/col469 {0.157 0.475 0.286 srgb} bind def
/col470 {0.875 0.157 0.125 srgb} bind def
/col471 {0.125 0.349 0.780 srgb} bind def
/col472 {0.969 0.984 0.969 srgb} bind def
/col473 {0.937 0.937 0.937 srgb} bind def
/col474 {0.906 0.906 0.906 srgb} bind def
/col475 {0.000 0.380 0.286 srgb} bind def
/col476 {0.475 0.525 0.286 srgb} bind def
/col477 {0.843 0.843 0.843 srgb} bind def
/col478 {0.682 0.682 0.682 srgb} bind def
/col479 {0.380 0.443 0.475 srgb} bind def
/col480 {0.906 0.745 0.475 srgb} bind def
/col481 {0.557 0.620 0.475 srgb} bind def
/col482 {0.286 0.286 0.286 srgb} bind def
/col483 {0.651 0.714 0.780 srgb} bind def
/col484 {0.412 0.412 0.588 srgb} bind def
/col485 {0.525 0.412 0.412 srgb} bind def
/col486 {0.318 0.620 0.286 srgb} bind def
/col487 {0.843 0.906 0.906 srgb} bind def
/col488 {0.318 0.380 0.380 srgb} bind def
/col489 {0.094 0.412 0.286 srgb} bind def
/col490 {0.620 0.651 0.714 srgb} bind def
/col491 {0.125 0.525 0.349 srgb} bind def
/col492 {0.000 0.380 0.000 srgb} bind def
/col493 {0.349 0.412 0.220 srgb} bind def
/col494 {0.557 0.557 0.651 srgb} bind def
/col495 {0.969 0.745 0.349 srgb} bind def
/col496 {0.557 0.620 0.412 srgb} bind def
/col497 {0.380 0.380 0.380 srgb} bind def
/col498 {0.380 0.412 0.620 srgb} bind def
/col499 {0.380 0.380 0.380 srgb} bind def
/col500 {0.349 0.412 0.220 srgb} bind def
/col501 {0.843 0.843 0.843 srgb} bind def
/col502 {0.682 0.682 0.682 srgb} bind def
/col503 {0.557 0.557 0.651 srgb} bind def
/col504 {0.969 0.745 0.349 srgb} bind def
/col505 {0.557 0.620 0.412 srgb} bind def
/col506 {0.286 0.286 0.286 srgb} bind def
/col507 {0.380 0.380 0.380 srgb} bind def
/col508 {0.557 0.412 0.412 srgb} bind def
/col509 {0.349 0.349 0.349 srgb} bind def
/col510 {0.812 0.812 0.812 srgb} bind def
/col511 {0.255 0.271 0.255 srgb} bind def
/col512 {0.525 0.510 0.525 srgb} bind def
/col513 {0.745 0.765 0.745 srgb} bind def
/col514 {0.745 0.765 0.745 srgb} bind def
/col515 {0.525 0.510 0.525 srgb} bind def
/col516 {0.525 0.510 0.525 srgb} bind def
/col517 {0.745 0.765 0.745 srgb} bind def
/col518 {0.620 0.000 0.000 srgb} bind def
/col519 {0.620 0.000 0.000 srgb} bind def
/col520 {0.557 0.557 0.557 srgb} bind def
/col521 {0.255 0.255 0.255 srgb} bind def
/col522 {0.557 0.557 0.557 srgb} bind def
/col523 {0.255 0.255 0.255 srgb} bind def
/col524 {0.557 0.557 0.557 srgb} bind def
/col525 {0.255 0.255 0.255 srgb} bind def
/col526 {0.557 0.557 0.557 srgb} bind def
/col527 {0.255 0.255 0.255 srgb} bind def
/col528 {0.557 0.557 0.557 srgb} bind def
/col529 {0.255 0.255 0.255 srgb} bind def
/col530 {0.557 0.557 0.557 srgb} bind def
/col531 {0.255 0.255 0.255 srgb} bind def
/col532 {0.620 0.000 0.000 srgb} bind def
/col533 {0.620 0.000 0.000 srgb} bind def
/col534 {0.745 0.765 0.745 srgb} bind def
/col535 {0.412 0.427 0.412 srgb} bind def
/col536 {0.745 0.765 0.745 srgb} bind def
/col537 {0.412 0.427 0.412 srgb} bind def
/col538 {0.286 0.271 0.286 srgb} bind def
/col539 {0.557 0.557 0.557 srgb} bind def
/col540 {0.412 0.427 0.412 srgb} bind def
/col541 {0.557 0.557 0.557 srgb} bind def
/col542 {0.745 0.765 0.745 srgb} bind def

end
save
newpath 0 174 moveto 0 0 lineto 406 0 lineto 406 174 lineto closepath clip newpath
-36.0 188.0 translate
1 -1 scale

/cp {closepath} bind def
/ef {eofill} bind def
/gr {grestore} bind def
/gs {gsave} bind def
/sa {save} bind def
/rs {restore} bind def
/l {lineto} bind def
/m {moveto} bind def
/rm {rmoveto} bind def
/n {newpath} bind def
/s {stroke} bind def
/sh {show} bind def
/slc {setlinecap} bind def
/slj {setlinejoin} bind def
/slw {setlinewidth} bind def
/srgb {setrgbcolor} bind def
/rot {rotate} bind def
/sc {scale} bind def
/sd {setdash} bind def
/ff {findfont} bind def
/sf {setfont} bind def
/scf {scalefont} bind def
/sw {stringwidth} bind def
/tr {translate} bind def
/tnt {dup dup currentrgbcolor
  4 -2 roll dup 1 exch sub 3 -1 roll mul add
  4 -2 roll dup 1 exch sub 3 -1 roll mul add
  4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb}
  bind def
/shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul
  4 -2 roll mul srgb} bind def
/reencdict 12 dict def /ReEncode { reencdict begin
/newcodesandnames exch def /newfontname exch def /basefontname exch def
/basefontdict basefontname findfont def /newfont basefontdict maxlength dict def
basefontdict { exch dup /FID ne { dup /Encoding eq
{ exch dup length array copy newfont 3 1 roll put }
{ exch newfont 3 1 roll put } ifelse } { pop pop } ifelse } forall
newfont /FontName newfontname put newcodesandnames aload pop
128 1 255 { newfont /Encoding get exch /.notdef put } for
newcodesandnames length 2 idiv { newfont /Encoding get 3 1 roll put } repeat
newfontname newfont definefont pop end } def
/isovec [
8#055 /minus 8#200 /grave 8#201 /acute 8#202 /circumflex 8#203 /tilde
8#204 /macron 8#205 /breve 8#206 /dotaccent 8#207 /dieresis
8#210 /ring 8#211 /cedilla 8#212 /hungarumlaut 8#213 /ogonek 8#214 /caron
8#220 /dotlessi 8#230 /oe 8#231 /OE
8#240 /space 8#241 /exclamdown 8#242 /cent 8#243 /sterling
8#244 /currency 8#245 /yen 8#246 /brokenbar 8#247 /section 8#250 /dieresis
8#251 /copyright 8#252 /ordfeminine 8#253 /guillemotleft 8#254 /logicalnot
8#255 /hyphen 8#256 /registered 8#257 /macron 8#260 /degree 8#261 /plusminus
8#262 /twosuperior 8#263 /threesuperior 8#264 /acute 8#265 /mu 8#266 /paragraph
8#267 /periodcentered 8#270 /cedilla 8#271 /onesuperior 8#272 /ordmasculine
8#273 /guillemotright 8#274 /onequarter 8#275 /onehalf
8#276 /threequarters 8#277 /questiondown 8#300 /Agrave 8#301 /Aacute
8#302 /Acircumflex 8#303 /Atilde 8#304 /Adieresis 8#305 /Aring
8#306 /AE 8#307 /Ccedilla 8#310 /Egrave 8#311 /Eacute
8#312 /Ecircumflex 8#313 /Edieresis 8#314 /Igrave 8#315 /Iacute
8#316 /Icircumflex 8#317 /Idieresis 8#320 /Eth 8#321 /Ntilde 8#322 /Ograve
8#323 /Oacute 8#324 /Ocircumflex 8#325 /Otilde 8#326 /Odieresis 8#327 /multiply
8#330 /Oslash 8#331 /Ugrave 8#332 /Uacute 8#333 /Ucircumflex
8#334 /Udieresis 8#335 /Yacute 8#336 /Thorn 8#337 /germandbls 8#340 /agrave
8#341 /aacute 8#342 /acircumflex 8#343 /atilde 8#344 /adieresis 8#345 /aring
8#346 /ae 8#347 /ccedilla 8#350 /egrave 8#351 /eacute
8#352 /ecircumflex 8#353 /edieresis 8#354 /igrave 8#355 /iacute
8#356 /icircumflex 8#357 /idieresis 8#360 /eth 8#361 /ntilde 8#362 /ograve
8#363 /oacute 8#364 /ocircumflex 8#365 /otilde 8#366 /odieresis 8#367 /divide
8#370 /oslash 8#371 /ugrave 8#372 /uacute 8#373 /ucircumflex
8#374 /udieresis 8#375 /yacute 8#376 /thorn 8#377 /ydieresis] def
/Times-Bold /Times-Bold-iso isovec ReEncode
/Times-Italic /Times-Italic-iso isovec ReEncode
 /DrawEllipse {
	/endangle exch def
	/startangle exch def
	/yrad exch def
	/xrad exch def
	/y exch def
	/x exch def
	/savematrix mtrx currentmatrix def
	x y tr xrad yrad sc 0 0 1 startangle endangle arc
	closepath
	savematrix setmatrix
	} def

/$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def
/$F2psEnd {$F2psEnteredState restore end} def

$F2psBegin
%%Page: 1 1
10 setmiterlimit
 0.06000 0.06000 sc
%
% Fig objects follow
%
/Times-Italic-iso ff 210.00 scf sf
620 2282 m
gs 1 -1 sc (x) col0 sh gr
/Times-Italic-iso ff 150.00 scf sf
740 2342 m
gs 1 -1 sc (1) col0 sh gr
/Times-Italic-iso ff 210.00 scf sf
4257 2454 m
gs 1 -1 sc (x) col0 sh gr
/Times-Italic-iso ff 150.00 scf sf
4377 2514 m
gs 1 -1 sc (1) col0 sh gr
% Polyline
7.500 slw
n 3816 1665 m
 4100 1665 l gs col0 s gr 
% Polyline
n 3816 2265 m
 4100 2265 l gs col0 s gr 
% Polyline
n 3816 1875 m
 4100 1875 l gs col0 s gr 
/Symbol ff 195.00 scf sf
4169 2150 m
gs 1 -1 sc (e) col0 sh gr
/Times-Italic-iso ff 195.00 scf sf
4049 2150 m
gs 1 -1 sc (2) col0 sh gr
% Polyline
gs  clippath
3988 1869 m 3946 1869 l 3946 1941 l 3967 1893 l 3988 1941 l cp
3946 2273 m 3988 2273 l 3988 2200 l 3967 2249 l 3946 2200 l cp
eoclip
n 3967 2258 m
 3967 1884 l gs col0 s gr gr

% arrowhead
n 3946 2200 m 3967 2249 l 3988 2200 l 3967 2184 l 3946 2200 l 
 cp gs 0.00 setgray ef gr  col0 s
% arrowhead
n 3988 1941 m 3967 1893 l 3946 1941 l 3967 1957 l 3988 1941 l 
 cp gs 0.00 setgray ef gr  col0 s
/Symbol ff 195.00 scf sf
4049 1828 m
gs 1 -1 sc (e) col0 sh gr
% Polyline
gs  clippath
3988 1659 m 3946 1659 l 3946 1731 l 3967 1683 l 3988 1731 l cp
3946 1887 m 3988 1887 l 3988 1814 l 3967 1863 l 3946 1814 l cp
eoclip
n 3967 1872 m
 3967 1674 l gs col0 s gr gr

% arrowhead
n 3946 1814 m 3967 1863 l 3988 1814 l 3967 1798 l 3946 1814 l 
 cp gs 0.00 setgray ef gr  col0 s
% arrowhead
n 3988 1731 m 3967 1683 l 3946 1731 l 3967 1747 l 3988 1731 l 
 cp gs 0.00 setgray ef gr  col0 s
/Times-Italic-iso ff 240.00 scf sf
4550 2847 m
gs 1 -1 sc (z) col0 sh gr
/Times-Italic-iso ff 150.00 scf sf
4683 2914 m
gs 1 -1 sc (1) col0 sh gr
/Times-Italic-iso ff 240.00 scf sf
4347 1143 m
gs 1 -1 sc (z) col0 sh gr
/Times-Italic-iso ff 150.00 scf sf
4480 1210 m
gs 1 -1 sc (2) col0 sh gr
/Times-Italic-iso ff 240.00 scf sf
6952 1153 m
gs 1 -1 sc (z) col0 sh gr
/Times-Italic-iso ff 150.00 scf sf
7084 1218 m
gs 1 -1 sc (3) col0 sh gr
/Times-Italic-iso ff 210.00 scf sf
1567 517 m
gs 1 -1 sc (x) col0 sh gr
/Times-Italic-iso ff 150.00 scf sf
1687 577 m
gs 1 -1 sc (3) col0 sh gr
/Times-Italic-iso ff 210.00 scf sf
600 1530 m
gs 1 -1 sc (y) col0 sh gr
/Times-Italic-iso ff 150.00 scf sf
720 1590 m
gs 1 -1 sc (2) col0 sh gr
/Times-Italic-iso ff 210.00 scf sf
3517 2452 m
gs 1 -1 sc (y) col0 sh gr
/Times-Italic-iso ff 150.00 scf sf
3637 2512 m
gs 1 -1 sc (1) col0 sh gr
/Times-Italic-iso ff 210.00 scf sf
7157 2287 m
gs 1 -1 sc (y) col0 sh gr
/Times-Italic-iso ff 150.00 scf sf
7277 2347 m
gs 1 -1 sc (1) col0 sh gr
/Times-Italic-iso ff 210.00 scf sf
3517 1485 m
gs 1 -1 sc (x) col0 sh gr
/Times-Italic-iso ff 150.00 scf sf
3637 1545 m
gs 1 -1 sc (2) col0 sh gr
/Times-Italic-iso ff 210.00 scf sf
4170 1485 m
gs 1 -1 sc (y) col0 sh gr
/Times-Italic-iso ff 150.00 scf sf
4290 1545 m
gs 1 -1 sc (2) col0 sh gr
/Times-Italic-iso ff 210.00 scf sf
7138 1485 m
gs 1 -1 sc (x) col0 sh gr
/Times-Italic-iso ff 150.00 scf sf
7258 1545 m
gs 1 -1 sc (2) col0 sh gr
/Times-Italic-iso ff 210.00 scf sf
2565 510 m
gs 1 -1 sc (y) col0 sh gr
/Times-Italic-iso ff 150.00 scf sf
2685 570 m
gs 1 -1 sc (3) col0 sh gr
/Times-Italic-iso ff 210.00 scf sf
5178 495 m
gs 1 -1 sc (x) col0 sh gr
/Times-Italic-iso ff 150.00 scf sf
5298 555 m
gs 1 -1 sc (3) col0 sh gr
/Times-Italic-iso ff 210.00 scf sf
6186 510 m
gs 1 -1 sc (y) col0 sh gr
/Times-Italic-iso ff 150.00 scf sf
6306 570 m
gs 1 -1 sc (3) col0 sh gr
% Polyline
n 6005 577 m
 6005 337 l gs col0 s gr 
% Polyline
n 5555 584 m
 5555 344 l gs col0 s gr 
% Polyline
 [15 60] 60 sd
n 4625 2275 m 6983 1675 l 5558 672 l
 cp gs col0 s gr  [] 0 sd
% Polyline
gs  clippath
5999 439 m 5999 397 l 5926 397 l 5975 418 l 5926 439 l cp
5770 397 m 5770 439 l 5842 439 l 5794 418 l 5842 397 l cp
eoclip
n 5785 418 m
 5984 418 l gs col0 s gr gr

% arrowhead
n 5842 397 m 5794 418 l 5842 439 l 5858 418 l 5842 397 l 
 cp gs 0.00 setgray ef gr  col0 s
% arrowhead
n 5926 439 m 5975 418 l 5926 397 l 5910 418 l 5926 439 l 
 cp gs 0.00 setgray ef gr  col0 s
% Polyline
gs  clippath
5777 439 m 5777 397 l 5704 397 l 5753 418 l 5704 439 l cp
5549 397 m 5549 439 l 5621 439 l 5573 418 l 5621 397 l cp
eoclip
n 5564 418 m
 5762 418 l gs col0 s gr gr

% arrowhead
n 5621 397 m 5573 418 l 5621 439 l 5637 418 l 5621 397 l 
 cp gs 0.00 setgray ef gr  col0 s
% arrowhead
n 5704 439 m 5753 418 l 5704 397 l 5688 418 l 5704 439 l 
 cp gs 0.00 setgray ef gr  col0 s
% Polyline
 [15 45] 45 sd
n 4701 1277 m 4822 2669 l 6838 1277 l
 cp gs col0 s gr  [] 0 sd
% Polyline
n 5780 666 m
 5780 3098 l gs col0 s gr 
% Polyline
 [15 60] 60 sd
n 1005 2280 m 3360 1675 l 1935 670 l
 cp gs col0 s gr  [] 0 sd
/Symbol ff 195.00 scf sf
2010 332 m
gs 1 -1 sc (e) col0 sh gr
/Symbol ff 195.00 scf sf
2227 331 m
gs 1 -1 sc (e) col0 sh gr
/Times-Bold-iso ff 210.00 scf sf
2025 1824 m
gs 1 -1 sc (0) col0 sh gr
/Symbol ff 195.00 scf sf
5630 331 m
gs 1 -1 sc (e) col0 sh gr
/Symbol ff 195.00 scf sf
5847 330 m
gs 1 -1 sc (e) col0 sh gr
/Times-Bold-iso ff 210.00 scf sf
5645 1823 m
gs 1 -1 sc (0) col0 sh gr
/Times-Italic-iso ff 240.00 scf sf
3147 924 m
gs 1 -1 sc (-z) col0 sh gr
/Times-Italic-iso ff 240.00 scf sf
730 2685 m
gs 1 -1 sc (-z) col0 sh gr
/Times-Italic-iso ff 150.00 scf sf
3420 1020 m
gs 1 -1 sc (1) col0 sh gr
/Times-Italic-iso ff 240.00 scf sf
3262 2677 m
gs 1 -1 sc (-z) col0 sh gr
/Times-Italic-iso ff 150.00 scf sf
1005 2782 m
gs 1 -1 sc (3) col0 sh gr
/Times-Italic-iso ff 150.00 scf sf
3522 2759 m
gs 1 -1 sc (2) col0 sh gr
15.000 slw
% Ellipse
n 5771 1882 1224 1224 0 360 DrawEllipse gs col0 s gr

% Ellipse
n 2151 1883 1224 1224 0 360 DrawEllipse gs col0 s gr

% Polyline
7.500 slw
n 927 1883 m
 3375 1883 l gs col0 s gr 
% Polyline
n 2160 666 m
 2160 3099 l gs col0 s gr 
% Polyline
n 2160 578 m
 2160 338 l gs col0 s gr 
% Polyline
n 2385 578 m
 2385 338 l gs col0 s gr 
% Polyline
n 1935 585 m
 1935 345 l gs col0 s gr 
% Polyline
gs  clippath
2379 440 m 2379 398 l 2306 398 l 2355 419 l 2306 440 l cp
2150 398 m 2150 440 l 2222 440 l 2174 419 l 2222 398 l cp
eoclip
n 2165 419 m
 2364 419 l gs col0 s gr gr

% arrowhead
n 2222 398 m 2174 419 l 2222 440 l 2238 419 l 2222 398 l 
 cp gs 0.00 setgray ef gr  col0 s
% arrowhead
n 2306 440 m 2355 419 l 2306 398 l 2290 419 l 2306 440 l 
 cp gs 0.00 setgray ef gr  col0 s
% Polyline
gs  clippath
2157 440 m 2157 398 l 2084 398 l 2133 419 l 2084 440 l cp
1929 398 m 1929 440 l 2001 440 l 1953 419 l 2001 398 l cp
eoclip
n 1944 419 m
 2142 419 l gs col0 s gr gr

% arrowhead
n 2001 398 m 1953 419 l 2001 440 l 2017 419 l 2001 398 l 
 cp gs 0.00 setgray ef gr  col0 s
% arrowhead
n 2084 440 m 2133 419 l 2084 398 l 2068 419 l 2084 440 l 
 cp gs 0.00 setgray ef gr  col0 s
% Polyline
n 4547 1882 m
 6995 1882 l gs col0 s gr 
% Polyline
n 5780 577 m
 5780 337 l gs col0 s gr 
% Polyline
 [15 60] 60 sd
n 2386 667 m 947 1661 l 3300 2265 l
 cp gs col0 s gr  [] 0 sd
% Polyline
 [15 60] 60 sd
n 6003 667 m 4565 1661 l 6922 2261 l
 cp gs col0 s gr  [] 0 sd
% Ellipse
n 4565 1657 65 65 0 360 DrawEllipse gs col7 1.00 shd ef gr gs col0 s gr

% Ellipse
n 6920 2257 65 65 0 360 DrawEllipse gs col7 1.00 shd ef gr gs col0 s gr

% Ellipse
n 6005 667 65 65 0 360 DrawEllipse gs col7 1.00 shd ef gr gs col0 s gr

% Ellipse
n 3300 2258 65 65 0 360 DrawEllipse gs col7 1.00 shd ef gr gs col0 s gr

% Polyline
n 4629 1275 m 4703 1201 l 4777 1275 l 4703 1349 l
 cp gs col7 1.00 shd ef gr gs col0 s gr 
% Polyline
n 6762 1277 m 6836 1203 l 6910 1277 l 6836 1351 l
 cp gs col7 1.00 shd ef gr gs col0 s gr 
% Polyline
n 4565 2332 m 4685 2332 l 4685 2212 l 4565 2212 l
 cp gs col7 1.00 shd ef gr gs col0 s gr 
% Polyline
n 945 2333 m 1065 2333 l 1065 2213 l 945 2213 l
 cp gs col7 1.00 shd ef gr gs col0 s gr 
% Polyline
n 1875 728 m 1995 728 l 1995 608 l 1875 608 l
 cp gs col7 1.00 shd ef gr gs col0 s gr 
% Polyline
n 3139 2486 m 3213 2412 l 3287 2486 l 3213 2560 l
 cp gs col7 0.70 shd ef gr gs col0 s gr 
% Polyline
n 3300 1733 m 3420 1733 l 3420 1613 l 3300 1613 l
 cp gs col7 1.00 shd ef gr gs col0 s gr 
% Polyline
n 2972 1045 m 3046 971 l 3120 1045 l 3046 1119 l
 cp gs col7 0.70 shd ef gr gs col0 s gr 
% Polyline
n 4749 2670 m 4823 2596 l 4897 2670 l 4823 2744 l
 cp gs col7 1.00 shd ef gr gs col0 s gr 
% Polyline
n 1013 2476 m 1087 2402 l 1161 2476 l 1087 2550 l
 cp gs col7 0.70 shd ef gr gs col0 s gr 
% Polyline
n 5495 727 m 5615 727 l 5615 607 l 5495 607 l
 cp gs col7 1.00 shd ef gr gs col0 s gr 
% Ellipse
n 945 1658 65 65 0 360 DrawEllipse gs col7 1.00 shd ef gr gs col0 s gr

% Ellipse
n 2385 668 65 65 0 360 DrawEllipse gs col7 1.00 shd ef gr gs col0 s gr

% Polyline
n 6920 1732 m 7040 1732 l 7040 1612 l 6920 1612 l
 cp gs col7 1.00 shd ef gr gs col0 s gr 
$F2psEnd
rs

%%EndDocument
 @endspecial 393 2413 a Ft(Figure)37 b(4.)49 b Fu(V)-8
b(alid)32 b(con\014guration)h FA(S)1815 2377 y Fj(\000)1907
2413 y Fu(in)g(dimension)h(2)e(with)h FA(depth)3067 2437
y Fh(S)3112 2418 y Fe(\000)3168 2413 y Fu(\()p FA(0)p
Fu(\))28 b(=)f(5.)100 2664 y(Using)f(the)h(analysis)g(in)f(Section)h
(3.5)f(w)m(e)h(see)g(that)f(the)g(cells)i(generated)e(b)m(y)h
Fs(X)34 b Fu(and)26 b Fs(Y)47 b Fu(ha)m(v)m(e)28 b(colourful)0
2780 y(co)m(v)m(ering)37 b(depth)f(at)e(least)i(1.)51
b(If)35 b(no)g(cell)h(attains)f(this,)i(then)f(our)f(con\014guration)g
(m)m(ust)h(yield)h(at)d(least)0 2896 y(6)39 b(colourful)h(simplices)i
(con)m(taining)e FA(0)p Fu(.)65 b(If)39 b(some)h(cell)h(has)f(depth)g
(1,)h(w)m(e)g(can)f(place)g(at)f(most)h(t)m(w)m(o)g(of)0
3012 y(the)35 b Fn(\000)p Fs(z)292 3027 y Fq(i)321 3012
y Fu('s)g(in)g(this)g(cell.)50 b(The)36 b(remaining)f
Fs(z)1651 3027 y Fq(i)1714 3012 y Fu(m)m(ust)g(then)h(ha)m(v)m(e)f
(depth)h(at)e(least)h(2,)g(for)f(a)g(minim)m(um)i(of)0
3128 y(4.)59 b(In)38 b(fact,)h(w)m(e)g(can)f(strengthen)h(this)g(to)e
(sho)m(w)i(that)e(our)h(con\014guration)g(is)g(minimal)h(b)m(y)g
(observing)0 3245 y(that)d(w)m(e)h(cannot)f(place)g(all)g(of)f
Fs(Z)43 b Fu(in)36 b(t)m(w)m(o)h(adjacen)m(t)f(cells.)55
b(W)-8 b(e)36 b(conclude)i(that)d Fs(\026)p Fu(\(2\))e(=)g(5.)53
b(A)36 b(similar)0 3361 y(observ)-5 b(ation)33 b(in)h(three)f
(dimensions)i(sho)m(ws)g(that)d Fs(\026)p Fu(\(3\))c
Fn(\025)h Fu(8.)44 b(Giv)m(en)34 b(the)f(construction)h(of)f(Section)g
(3.4)0 3477 y(and)c(Prop)s(osition)h(3.4)f(w)m(e)h(kno)m(w)h(that)e
Fs(\026)p Fu(\(3\))f(is)i(either)g(8)f(or)g(10.)42 b(B\023)-49
b(ar\023)g(an)m(y)30 b(and)g(Matou)-5 b(\024)-44 b(sek)30
b([BM05])g(ha)m(v)m(e)0 3593 y(sho)m(wn)k(that)e Fs(\026)p
Fu(\(3\))27 b Fn(\025)h Fu(9)33 b(whic)m(h)h(com)m(bined)g(with)f(Prop)
s(osition)g(3.4)f(implies)i(that)f Fs(\026)p Fu(\(3\))27
b(=)g(10.)1578 3810 y(4.)49 b Ft(Conclusions)100 3985
y Fu(Let)35 b(us)h(return)g(to)f(our)g(original)g(goals.)52
b(Using)36 b(the)g(b)s(ound)f Fs(\026)p Fu(\()p Fs(d)p
Fu(\))d Fn(\025)h Fu(2)p Fs(d)h Fu(from)i(Section)g(3.5,)f(w)m(e)i(see)
0 4101 y(that)d(w)m(e)i(can)f(impro)m(v)m(e)h(B\023)-49
b(ar\023)g(an)m(y's)36 b(lo)m(w)m(er)f(b)s(ound)g(\(5\))f(for)g(the)h
(depth)h(of)e(the)h(mono)s(c)m(hrome)g(simplicial)0 4217
y(median)e(to:)1195 4377 y Fs(g)t Fu(\()p Fs(S)6 b Fu(\))27
b Fn(\025)1694 4309 y Fu(2)p Fs(d)p 1530 4354 427 4 v
1530 4445 a Fu(\()p Fs(d)22 b Fu(+)g(1\))1826 4416 y
Fq(d)p Fo(+1)1966 4236 y Fk(\022)2120 4309 y Fs(n)2040
4445 y(d)f Fu(+)h(1)2259 4236 y Fk(\023)2355 4377 y Fu(+)g
Fs(O)s Fu(\()p Fs(n)2627 4336 y Fq(d)2667 4377 y Fu(\))1070
b(\(8\))0 4576 y(This)40 b(is)f(a)f(mo)s(dest)i(impro)m(v)m(emen)m(t.)
64 b(Unfortunately)-8 b(,)41 b(the)e(construction)h(in)f(Section)h(3.4)
e(sho)m(ws)i(that)0 4692 y(simply)34 b(b)s(ounding)f
Fs(\026)p Fu(\()p Fs(d)p Fu(\))f(cannot)h(giv)m(e)g(a)f(stronger)h(b)s
(ound)g(than:)1195 4919 y Fs(g)t Fu(\()p Fs(S)6 b Fu(\))27
b Fn(\025)1614 4852 y Fs(d)1665 4816 y Fo(2)1726 4852
y Fu(+)22 b(1)p 1530 4897 V 1530 4988 a(\()p Fs(d)g Fu(+)g(1\))1826
4959 y Fq(d)p Fo(+1)1966 4779 y Fk(\022)2120 4852 y Fs(n)2040
4988 y(d)f Fu(+)h(1)2259 4779 y Fk(\023)2355 4919 y Fu(+)g
Fs(O)s Fu(\()p Fs(n)2627 4878 y Fq(d)2667 4919 y Fu(\))1070
b(\(9\))100 5145 y(Quite)26 b(recen)m(tly)-8 b(,)29 b(W)-8
b(agner)26 b(pro)m(v)m(ed)h(exactly)h(the)e(b)s(ound)g(\(9\))f(in)h
(his)h(thesis)g([W)-8 b(ag03])26 b(as)g(a)f(sp)s(ecial)i(case)0
5261 y(of)34 b(his)h(First)g(Selection)g(Lemma.)50 b(This)36
b(is,)f(to)f(our)h(kno)m(wledge,)i(the)d(\014rst)h(impro)m(v)m(emen)m
(t)j(of)33 b(\(5\))i(since)p eop end
%%Page: 14 14
TeXDict begin 14 13 bop 0 75 a Fl(14)498 b(ANTOINE)25
b(DEZA,)g(SUI)f(HUANG,)h(T)-6 b(AMON)25 b(STEPHEN)h(AND)e(T)-6
b(AM)2823 56 y(\023)2813 75 y(AS)25 b(TERLAKY)0 274 y
Fu(B\023)-49 b(ar\023)g(an)m(y's)44 b(original)e(pap)s(er)h([B\023)-49
b(ar82].)74 b(W)-8 b(agner's)43 b(result)h(uses)g(a)f(con)m(tin)m(uous)
i(v)m(ersion)f(of)e(the)h(Upp)s(er)0 390 y(Bound)34 b(Theorem)g(for)f
(p)s(olytop)s(es)h(and)g(other)f(tec)m(hniques)k(from)c(probabilit)m(y)
h(without)g(an)m(y)g(reference)0 506 y(to)45 b(colouring.)81
b(W)-8 b(e)45 b(\014nd)h(the)f(app)s(earance)h(of)e(the)i(constan)m(t)g
Fs(d)2484 470 y Fo(2)2554 506 y Fu(+)30 b(1,)48 b(whic)m(h)f(for)d(us)i
(arriv)m(es)g(from)0 623 y(colourful)33 b(com)m(binatorics,)h(quite)f
(remark)-5 b(able.)0 797 y(4.1.)49 b FA(Bounds)34 b(for)g(Core)f(P)m
(oin)m(t)h(Depth.)49 b Fu(Recalling)30 b(that)f(m\()p
FA(S)p Fu(\))h(is)g(the)f(minim)m(um)j(v)-5 b(alue)29
b(of)g(a)h(core)0 913 y(p)s(oin)m(t)c(in)h(a)e(con\014guration)i
FA(S)f Fu(and)g(that)g Fs(\026)p Fu(\()p Fs(d)p Fu(\))f(is)i(the)g
(minim)m(um)g(v)-5 b(alue)27 b(of)f(m\()p FA(S)p Fu(\))g(o)m(v)m(er)h
(all)f Fs(d)p Fu(-dimensional)0 1029 y(colourful)33 b(con\014gurations)
g FA(S)p Fu(,)g(our)f(main)h(result)h(is:)0 1199 y FA(Theorem)52
b(4.1.)c Fp(The)e(minimal)e(c)-5 b(olourful)46 b(simplicial)f(depth)g
(of)h(any)g(interior)g(c)-5 b(or)g(e)46 b(p)-5 b(oint)45
b(in)h(any)0 1315 y(c)-5 b(olourful)35 b(c)-5 b(on\014gur)g(ation)34
b(is)g(b)-5 b(etwe)g(en)35 b Fu(2)p Fs(d)f Fp(and)g Fs(d)1819
1279 y Fo(2)1880 1315 y Fu(+)22 b(1)p Fp(.)45 b(That)35
b(is,)f(we)h(have:)44 b Fu(2)p Fs(d)27 b Fn(\024)h Fs(\026)p
Fu(\()p Fs(d)p Fu(\))f Fn(\024)h Fs(d)3483 1279 y Fo(2)3544
1315 y Fu(+)22 b(1)p Fp(.)0 1485 y FA(Conjecture)37 b(4.2.)k
Fu(The)33 b(minim)m(um)h(colourful)e(simplicial)i(depth)f(of)e(an)m(y)i
(in)m(terior)f(core)h(p)s(oin)m(t)f(in)g(an)m(y)0 1601
y(colourful)h(con\014guration)f(is)i Fs(d)1144 1565 y
Fo(2)1205 1601 y Fu(+)22 b(1.)43 b(That)33 b(is,)g(w)m(e)h(ha)m(v)m(e)g
Fs(\026)p Fu(\()p Fs(d)p Fu(\))27 b(=)g Fs(d)2527 1565
y Fo(2)2588 1601 y Fu(+)22 b(1.)100 1771 y(This)h(conjecture)g(implies)
h(that)e(the)g(con\014guration)g FA(S)2091 1735 y Fj(\000)2172
1771 y Fu(minimizes)j(m\()p FA(S)p Fu(\))d(for)g Fs(d)p
Fu(-dimensional)g(colour-)0 1887 y(ful)35 b(con\014gurations.)50
b(It)35 b(w)m(ould)g(also)g(giv)m(e)h(an)e(elemen)m(tary)j(pro)s(of)d
(of)g(\(9\).)49 b(It)35 b(is)g(easy)h(to)e(see)i(that)e(this)0
2003 y(holds)g(for)e Fs(d)d Fu(=)f(1.)45 b(As)34 b(w)m(e)g(noted)g(in)f
(Section)h(3.6,)f(Conjecture)h(4.2)f(holds)h(for)e Fs(d)d
Fu(=)f(2)33 b(and)g Fs(d)c Fu(=)f(3.)45 b(The)0 2120
y(non-uniqueness)34 b(of)e(con\014gurations)g(attaining)g(m\()p
FA(S)p Fu(\))c(=)f Fs(d)2237 2083 y Fo(2)2297 2120 y
Fu(+)20 b(1)32 b(suggests)h(that)f(an)m(y)g(suc)m(h)h(pro)s(of)e(can-)0
2236 y(not)k(b)s(e)g(completely)h(trivial)g(but)f(it)g(ma)m(y)g(b)s(e)g
(p)s(ossible)h(to)f(do)g(this)g(through)g(impro)m(v)m(ed)i(b)s(o)s(okk)
m(eeping.)0 2352 y(The)28 b(authors)f(generated)h(random)f(lo)m
(w-dimensional)i(con\014gurations)f(b)m(y)g(computer)g(and)f(did)g(not)
g(\014nd)0 2468 y(an)m(y)33 b(coun)m(terexamples)j(to)c(Conjecture)i
(4.2.)0 2638 y Fp(R)-5 b(emark)35 b Fu(4.3)p Fp(.)e Fu(The)22
b(lo)m(w)m(er)h(b)s(ound)f(for)f Fs(\026)p Fu(\()p Fs(d)p
Fu(\))g(w)m(as)i(impro)m(v)m(ed)h(v)m(ery)f(recen)m(tly)h(indep)s
(enden)m(tly)g(b)m(y)f(B\023)-49 b(ar\023)g(an)m(y)22
b(and)0 2816 y(Matou)-5 b(\024)-44 b(sek)37 b([BM05)q(])f(and)g
(Stephen)i(and)e(Thomas)h([ST05])f(to)g(max)2570 2675
y Fk(\022)2644 2816 y Fu(3)p Fs(d;)2797 2748 y Fu(1)p
2797 2793 49 4 v 2797 2884 a(5)2856 2816 y Fs(d)p Fu(\()p
Fs(d)21 b Fu(+)h(1\))3202 2675 y Fk(\023)3311 2816 y
Fu(for)36 b Fs(d)d(>)h Fu(2)i(and)0 2924 y Fk(\026)68
2998 y Fu(\()p Fs(d)22 b Fu(+)g(2\))364 2961 y Fo(2)p
68 3042 335 4 v 211 3133 a Fu(4)413 2924 y Fk(\027)507
3065 y Fu(resp)s(ectiv)m(ely)-8 b(.)56 b(W)-8 b(e)36
b(kno)m(w)h(that)f Fs(\026)p Fu(\(1\))c(=)h(2,)j Fs(\026)p
Fu(\(2\))d(=)g(5)i(and)h Fs(\026)p Fu(\(3\))d(=)g(10.)52
b(Com)m(bining)38 b(the)0 3237 y(impro)m(v)m(ed)30 b(b)s(ounds)f(with)g
(the)f(parit)m(y)h(conditions)g(of)f(Prop)s(osition)h(3.4)e(w)m(e)j(ha)
m(v)m(e)f(the)g(follo)m(wing)f(b)s(ounds)0 3353 y(on)k
Fs(\026)p Fu(\()p Fs(d)p Fu(\))g(for)g Fs(d)c(>)f Fu(3:)534
3510 y(12)g Fn(\024)h Fs(\026)p Fu(\(4\))f Fn(\024)h
Fu(17)p Fs(;)49 b Fu(16)27 b Fn(\024)i Fs(\026)p Fu(\(5\))e
Fn(\024)h Fu(26)p Fs(;)49 b Fu(18)27 b Fn(\024)h Fs(\026)p
Fu(\(6\))f Fn(\024)h Fu(37)p Fs(;)49 b Fu(22)27 b Fn(\024)h
Fs(\026)p Fu(\(7\))f Fn(\024)h Fu(50)p Fs(;)0 3667 y
Fu(and)33 b(for)f Fs(d)27 b(>)h Fu(7:)1346 3684 y Fk(\026)1414
3757 y Fu(\()p Fs(d)22 b Fu(+)g(2\))1710 3721 y Fo(2)p
1414 3802 V 1557 3893 a Fu(4)1759 3684 y Fk(\027)1845
3824 y Fn(\024)28 b Fs(\026)p Fu(\()p Fs(d)p Fu(\))f
Fn(\024)h Fs(d)2319 3783 y Fo(2)2380 3824 y Fu(+)22 b(1)p
Fs(:)100 4074 y Fu(It)30 b(is)g(also)g(natural)g(to)f(ask)i(what)f(t)m
(yp)s(e)h(of)e(colourful)h(con\014guration)g(has)h(a)e(core)i(p)s(oin)m
(t)f(of)f Fp(maximum)0 4190 y Fu(colourful)35 b(simplicial)h(depth.)50
b(F)-8 b(or)34 b(this)h(question)h(to)e(b)s(e)h(in)m(teresting,)i(w)m
(e)e(m)m(ust)h(\014x)f(the)g(n)m(um)m(b)s(er)h(and)0
4306 y(size)j(of)f(the)h(colourful)f(sets.)61 b(Hence)40
b(w)m(e)f(restrict)g(our)f(atten)m(tion)g(to)g Fs(d)p
Fu(-con\014gurations)g(with)h(\()p Fs(d)25 b Fu(+)h(1\))0
4422 y(p)s(oin)m(ts)39 b(in)g(eac)m(h)g(of)f(\()p Fs(d)26
b Fu(+)g(1\))38 b(colours.)62 b(W)-8 b(e)39 b(also)f(require)i
Fs(p)e Fu(to)g(lie)h(in)g(the)g(in)m(terior)g(of)f(the)h(core)g(since)0
4539 y(mo)m(ving)33 b(to)g(the)g(b)s(oundary)g(of)f(a)g(simplex)j
(increases)f(the)f(depth.)44 b(W)-8 b(e)33 b(de\014ne:)1028
4695 y Fs(\027)6 b Fu(\()p Fs(d)p Fu(\))28 b(=)466 b(max)1340
4762 y Fq(d)24 b Fo(con\014gurations)h Fh(S)p Fq(;)32
b(p)p Fj(2)p Fo(in)n(t\(core)q(\()p Fh(S)p Fo(\)\))2416
4695 y FA(depth)2698 4719 y Fh(S)2747 4695 y Fu(\()p
Fs(p)p Fu(\))855 b(\(10\))100 4912 y(Our)31 b(metho)s(d)h(is)g(w)m(ell)
h(suited)g(to)e(analyzing)i Fs(\027)6 b Fu(\()p Fs(d)p
Fu(\))31 b(simply)i(b)m(y)g(c)m(hanging)f(our)g(ob)5
b(jectiv)m(e)33 b(to)f(creating)0 5028 y(deep)40 b(cells)h(and)e
(placing)h(an)m(tip)s(o)s(des)f(in)h(them.)64 b(W)-8
b(e)40 b(remark)f(that)g Fs(\027)6 b Fu(\(1\))39 b(=)g(2.)63
b(An)40 b(analysis)g(similar)0 5145 y(to)f(that)g(of)g(Section)h(3.6)f
(sho)m(ws)i(that)e Fs(\027)6 b Fu(\(2\))39 b(=)g(9.)63
b(The)41 b(k)m(ey)f(observ)-5 b(ation)40 b(is)g(after)f(placing)h(t)m
(w)m(o)g(sets)0 5261 y(of)d(three)i(colourful)f(p)s(oin)m(ts)g(on)g
(the)g(circle,)j(the)d(sequence)i(of)e(cell)g(depths)i(that)d(w)m(e)i
(obtain)f(is)g(either)p eop end
%%Page: 15 15
TeXDict begin 15 14 bop 1304 71 a Fl(COLOURFUL)32 b(SIMPLICIAL)g(DEPTH)
1227 b(15)0 274 y Fu(1,2,3,4,3,2)37 b(or)h(3,2,3,2,3,2.)60
b(In)38 b(the)h(\014rst)f(case)i(w)m(e)f(also)f(need)h(to)f(argue)g
(that)g(the)h(cells)h(of)d(depth)i(at)0 390 y(least)c(3)f(co)m(v)m(er)i
(less)f(than)g(half)f(the)h(circle)g(and)g(that)f(opp)s(osite)g(ev)m
(ery)j(p)s(oin)m(t)d(of)g(depth)h(4)f(is)h(a)f(p)s(oin)m(t)g(of)0
506 y(depth)f(1.)100 623 y(The)h(minimal)g(core)f(depth)h
(con\014guration)f FA(S)1817 586 y Fj(\000)1910 623 y
Fu(used)h(to)f(pro)m(v)m(e)h Fs(\026)p Fu(\(2\))28 b(=)h(5)k(is)g(top)s
(ologically)g(unique,)0 739 y(so)45 b(it)f(is)h(in)m(teresting)h(to)f
(observ)m(e)h(that,)h(up)e(to)g(top)s(ology)-8 b(,)46
b(there)g(are)e(t)m(w)m(o)i(distinct)f(con\014gurations)0
855 y(that)33 b(con)m(tain)h FA(0)f Fu(in)h(9)e(colourful)i(simplices.)
48 b(The)34 b(\014rst)g(corresp)s(onds)g(to)f(the)h(sequence)i(of)d
(cell)h(depths)0 971 y(1,2,3,4,3,2)j(and)g(con)m(tains)i(a)e(p)s(oin)m
(t)g Fs(z)1438 986 y Fo(3)1516 971 y Fu(that)g(generates)h(a)g(unique)h
FA(0)p Fu(-con)m(taining)e(colourful)h(simplex.)0 1087
y(The)32 b(second)g(corresp)s(onds)h(to)d(the)i(sequence)h(3,2,3,2,3,2)
d(and)i(is)f(a)g(com)m(binatorially)h(symmetric)h(con-)0
1204 y(\014guration)44 b(where)h(eac)m(h)g(colourful)f(p)s(oin)m(t)g
(is)g(in)g(exactly)i(three)e FA(0)p Fu(-con)m(taining)g(colourful)g
(simplices.)0 1320 y(The)34 b(con\014gurations)f(are)f(illustrated)i
(in)f(Figure)f(5.)710 2613 y @beginspecial 0 @llx 0 @lly
403 @urx 192 @ury 1417 @rhi @setspecial
%%BeginDocument: max2d.eps
%!PS-Adobe-2.0 EPSF-2.0
%%Title: max2d.eps
%%Creator: fig2dev Version 3.2 Patchlevel 3c
%%CreationDate: Fri May 27 15:25:39 2005
%%For: tamon@birkhoff (Tamon Stephen,TTCA)
%%BoundingBox: 0 0 403 192
%%Magnification: 1.0000
%%EndComments
/$F2psDict 200 dict def
$F2psDict begin
$F2psDict /mtrx matrix put
/col-1 {0 setgray} bind def
/col0 {0.000 0.000 0.000 srgb} bind def
/col1 {0.000 0.000 1.000 srgb} bind def
/col2 {0.000 1.000 0.000 srgb} bind def
/col3 {0.000 1.000 1.000 srgb} bind def
/col4 {1.000 0.000 0.000 srgb} bind def
/col5 {1.000 0.000 1.000 srgb} bind def
/col6 {1.000 1.000 0.000 srgb} bind def
/col7 {1.000 1.000 1.000 srgb} bind def
/col8 {0.000 0.000 0.560 srgb} bind def
/col9 {0.000 0.000 0.690 srgb} bind def
/col10 {0.000 0.000 0.820 srgb} bind def
/col11 {0.530 0.810 1.000 srgb} bind def
/col12 {0.000 0.560 0.000 srgb} bind def
/col13 {0.000 0.690 0.000 srgb} bind def
/col14 {0.000 0.820 0.000 srgb} bind def
/col15 {0.000 0.560 0.560 srgb} bind def
/col16 {0.000 0.690 0.690 srgb} bind def
/col17 {0.000 0.820 0.820 srgb} bind def
/col18 {0.560 0.000 0.000 srgb} bind def
/col19 {0.690 0.000 0.000 srgb} bind def
/col20 {0.820 0.000 0.000 srgb} bind def
/col21 {0.560 0.000 0.560 srgb} bind def
/col22 {0.690 0.000 0.690 srgb} bind def
/col23 {0.820 0.000 0.820 srgb} bind def
/col24 {0.500 0.190 0.000 srgb} bind def
/col25 {0.630 0.250 0.000 srgb} bind def
/col26 {0.750 0.380 0.000 srgb} bind def
/col27 {1.000 0.500 0.500 srgb} bind def
/col28 {1.000 0.630 0.630 srgb} bind def
/col29 {1.000 0.750 0.750 srgb} bind def
/col30 {1.000 0.880 0.880 srgb} bind def
/col31 {1.000 0.840 0.000 srgb} bind def
/col32 {0.412 0.427 0.412 srgb} bind def
/col33 {0.525 0.510 0.525 srgb} bind def
/col34 {0.745 0.765 0.745 srgb} bind def
/col35 {0.875 0.890 0.875 srgb} bind def
/col36 {0.525 0.510 0.525 srgb} bind def
/col37 {0.745 0.765 0.745 srgb} bind def
/col38 {0.875 0.890 0.875 srgb} bind def
/col39 {0.286 0.271 0.286 srgb} bind def
/col40 {0.286 0.271 0.286 srgb} bind def
/col41 {0.557 0.557 0.557 srgb} bind def
/col42 {0.620 0.000 0.000 srgb} bind def
/col43 {0.620 0.000 0.000 srgb} bind def
/col44 {0.557 0.557 0.557 srgb} bind def
/col45 {0.255 0.255 0.255 srgb} bind def
/col46 {0.557 0.557 0.557 srgb} bind def
/col47 {0.255 0.255 0.255 srgb} bind def
/col48 {0.557 0.557 0.557 srgb} bind def
/col49 {0.255 0.255 0.255 srgb} bind def
/col50 {0.557 0.557 0.557 srgb} bind def
/col51 {0.255 0.255 0.255 srgb} bind def
/col52 {0.557 0.557 0.557 srgb} bind def
/col53 {0.255 0.255 0.255 srgb} bind def
/col54 {0.557 0.557 0.557 srgb} bind def
/col55 {0.255 0.255 0.255 srgb} bind def
/col56 {0.557 0.557 0.557 srgb} bind def
/col57 {0.255 0.255 0.255 srgb} bind def
/col58 {0.557 0.557 0.557 srgb} bind def
/col59 {0.255 0.255 0.255 srgb} bind def
/col60 {0.557 0.557 0.557 srgb} bind def
/col61 {0.255 0.255 0.255 srgb} bind def
/col62 {0.557 0.557 0.557 srgb} bind def
/col63 {0.255 0.255 0.255 srgb} bind def
/col64 {0.557 0.557 0.557 srgb} bind def
/col65 {0.255 0.255 0.255 srgb} bind def
/col66 {0.557 0.557 0.557 srgb} bind def
/col67 {0.255 0.255 0.255 srgb} bind def
/col68 {0.557 0.557 0.557 srgb} bind def
/col69 {0.255 0.255 0.255 srgb} bind def
/col70 {0.557 0.557 0.557 srgb} bind def
/col71 {0.255 0.255 0.255 srgb} bind def
/col72 {0.557 0.557 0.557 srgb} bind def
/col73 {0.255 0.255 0.255 srgb} bind def
/col74 {0.557 0.557 0.557 srgb} bind def
/col75 {0.255 0.255 0.255 srgb} bind def
/col76 {0.557 0.557 0.557 srgb} bind def
/col77 {0.255 0.255 0.255 srgb} bind def
/col78 {0.557 0.557 0.557 srgb} bind def
/col79 {0.255 0.255 0.255 srgb} bind def
/col80 {0.745 0.765 0.745 srgb} bind def
/col81 {0.412 0.427 0.412 srgb} bind def
/col82 {0.745 0.765 0.745 srgb} bind def
/col83 {0.412 0.427 0.412 srgb} bind def
/col84 {0.286 0.271 0.286 srgb} bind def
/col85 {0.557 0.557 0.557 srgb} bind def
/col86 {0.412 0.427 0.412 srgb} bind def
/col87 {0.557 0.557 0.557 srgb} bind def
/col88 {0.443 0.443 0.443 srgb} bind def
/col89 {0.682 0.682 0.682 srgb} bind def
/col90 {0.188 0.188 0.188 srgb} bind def
/col91 {0.588 0.573 0.588 srgb} bind def
/col92 {0.443 0.443 0.443 srgb} bind def
/col93 {0.349 0.333 0.349 srgb} bind def
/col94 {0.682 0.698 0.682 srgb} bind def
/col95 {0.745 0.765 0.745 srgb} bind def
/col96 {0.286 0.271 0.286 srgb} bind def
/col97 {0.412 0.427 0.412 srgb} bind def
/col98 {0.286 0.271 0.286 srgb} bind def
/col99 {0.412 0.427 0.412 srgb} bind def
/col100 {0.745 0.765 0.745 srgb} bind def
/col101 {0.412 0.427 0.412 srgb} bind def
/col102 {0.286 0.271 0.286 srgb} bind def
/col103 {0.745 0.765 0.745 srgb} bind def
/col104 {0.412 0.427 0.412 srgb} bind def
/col105 {0.745 0.765 0.745 srgb} bind def
/col106 {0.286 0.271 0.286 srgb} bind def
/col107 {0.557 0.557 0.557 srgb} bind def
/col108 {0.875 0.890 0.937 srgb} bind def
/col109 {0.588 0.588 0.620 srgb} bind def
/col110 {0.843 0.859 0.843 srgb} bind def
/col111 {0.620 0.635 0.714 srgb} bind def
/col112 {0.620 0.000 0.000 srgb} bind def
/col113 {0.937 0.937 0.937 srgb} bind def
/col114 {0.875 0.890 0.875 srgb} bind def
/col115 {0.525 0.682 1.000 srgb} bind def
/col116 {0.443 0.443 1.000 srgb} bind def
/col117 {0.620 0.000 0.000 srgb} bind def
/col118 {0.620 0.000 0.000 srgb} bind def
/col119 {0.557 0.557 0.557 srgb} bind def
/col120 {0.255 0.255 0.255 srgb} bind def
/col121 {0.557 0.557 0.557 srgb} bind def
/col122 {0.255 0.255 0.255 srgb} bind def
/col123 {0.557 0.557 0.557 srgb} bind def
/col124 {0.255 0.255 0.255 srgb} bind def
/col125 {0.557 0.557 0.557 srgb} bind def
/col126 {0.255 0.255 0.255 srgb} bind def
/col127 {0.557 0.557 0.557 srgb} bind def
/col128 {0.255 0.255 0.255 srgb} bind def
/col129 {0.557 0.557 0.557 srgb} bind def
/col130 {0.255 0.255 0.255 srgb} bind def
/col131 {0.557 0.557 0.557 srgb} bind def
/col132 {0.255 0.255 0.255 srgb} bind def
/col133 {0.557 0.557 0.557 srgb} bind def
/col134 {0.255 0.255 0.255 srgb} bind def
/col135 {0.557 0.557 0.557 srgb} bind def
/col136 {0.255 0.255 0.255 srgb} bind def
/col137 {0.557 0.557 0.557 srgb} bind def
/col138 {0.255 0.255 0.255 srgb} bind def
/col139 {0.557 0.557 0.557 srgb} bind def
/col140 {0.255 0.255 0.255 srgb} bind def
/col141 {0.557 0.557 0.557 srgb} bind def
/col142 {0.255 0.255 0.255 srgb} bind def
/col143 {0.557 0.557 0.557 srgb} bind def
/col144 {0.255 0.255 0.255 srgb} bind def
/col145 {0.557 0.557 0.557 srgb} bind def
/col146 {0.255 0.255 0.255 srgb} bind def
/col147 {0.557 0.557 0.557 srgb} bind def
/col148 {0.255 0.255 0.255 srgb} bind def
/col149 {0.557 0.557 0.557 srgb} bind def
/col150 {0.255 0.255 0.255 srgb} bind def
/col151 {0.557 0.557 0.557 srgb} bind def
/col152 {0.255 0.255 0.255 srgb} bind def
/col153 {0.557 0.557 0.557 srgb} bind def
/col154 {0.255 0.255 0.255 srgb} bind def
/col155 {0.745 0.765 0.745 srgb} bind def
/col156 {0.412 0.427 0.412 srgb} bind def
/col157 {0.745 0.765 0.745 srgb} bind def
/col158 {0.412 0.427 0.412 srgb} bind def
/col159 {0.286 0.271 0.286 srgb} bind def
/col160 {0.557 0.557 0.557 srgb} bind def
/col161 {0.412 0.427 0.412 srgb} bind def
/col162 {0.557 0.557 0.557 srgb} bind def
/col163 {0.188 0.188 0.188 srgb} bind def
/col164 {0.588 0.573 0.588 srgb} bind def
/col165 {0.443 0.443 0.443 srgb} bind def
/col166 {0.349 0.333 0.349 srgb} bind def
/col167 {0.682 0.698 0.682 srgb} bind def
/col168 {0.745 0.765 0.745 srgb} bind def
/col169 {0.286 0.271 0.286 srgb} bind def
/col170 {0.412 0.427 0.412 srgb} bind def
/col171 {0.286 0.271 0.286 srgb} bind def
/col172 {0.412 0.427 0.412 srgb} bind def
/col173 {0.745 0.765 0.745 srgb} bind def
/col174 {0.412 0.427 0.412 srgb} bind def
/col175 {0.286 0.271 0.286 srgb} bind def
/col176 {0.745 0.765 0.745 srgb} bind def
/col177 {0.412 0.427 0.412 srgb} bind def
/col178 {0.745 0.765 0.745 srgb} bind def
/col179 {0.286 0.271 0.286 srgb} bind def
/col180 {0.557 0.557 0.557 srgb} bind def
/col181 {0.875 0.620 0.557 srgb} bind def
/col182 {0.937 0.937 0.875 srgb} bind def
/col183 {0.745 0.765 0.745 srgb} bind def
/col184 {0.875 0.796 0.682 srgb} bind def
/col185 {0.875 0.890 0.875 srgb} bind def
/col186 {0.812 0.827 0.812 srgb} bind def
/col187 {0.937 0.937 0.937 srgb} bind def
/col188 {0.843 0.475 0.094 srgb} bind def
/col189 {0.937 0.906 0.094 srgb} bind def
/col190 {0.557 0.490 0.745 srgb} bind def
/col191 {0.843 0.843 0.843 srgb} bind def
/col192 {0.557 0.557 0.651 srgb} bind def
/col193 {0.286 0.286 0.286 srgb} bind def
/col194 {0.557 0.412 0.412 srgb} bind def
/col195 {0.349 0.349 0.349 srgb} bind def
/col196 {0.380 0.380 0.380 srgb} bind def
/col197 {0.714 0.604 0.443 srgb} bind def
/col198 {0.255 0.573 1.000 srgb} bind def
/col199 {0.745 0.443 0.220 srgb} bind def
/col200 {0.843 0.459 0.000 srgb} bind def
/col201 {0.843 0.729 0.000 srgb} bind def
/col202 {0.000 0.396 0.000 srgb} bind def
/col203 {0.349 0.412 0.220 srgb} bind def
/col204 {0.812 0.827 0.812 srgb} bind def
/col205 {0.682 0.667 0.682 srgb} bind def
/col206 {0.557 0.557 0.651 srgb} bind def
/col207 {0.937 0.729 0.349 srgb} bind def
/col208 {0.557 0.604 0.412 srgb} bind def
/col209 {0.286 0.286 0.286 srgb} bind def
/col210 {0.380 0.396 0.380 srgb} bind def
/col211 {0.843 0.843 0.843 srgb} bind def
/col212 {0.557 0.557 0.651 srgb} bind def
/col213 {0.349 0.349 0.349 srgb} bind def
/col214 {0.380 0.380 0.380 srgb} bind def
/col215 {0.714 0.906 1.000 srgb} bind def
/col216 {0.525 0.765 0.937 srgb} bind def
/col217 {0.745 0.745 0.745 srgb} bind def
/col218 {0.812 0.588 0.318 srgb} bind def
/col219 {0.620 0.827 1.000 srgb} bind def
/col220 {0.843 0.843 0.843 srgb} bind def
/col221 {0.557 0.557 0.651 srgb} bind def
/col222 {0.557 0.412 0.412 srgb} bind def
/col223 {0.349 0.349 0.349 srgb} bind def
/col224 {0.380 0.380 0.380 srgb} bind def
/col225 {0.557 0.620 0.412 srgb} bind def
/col226 {0.969 0.412 0.000 srgb} bind def
/col227 {0.349 0.412 0.220 srgb} bind def
/col228 {0.557 0.620 0.412 srgb} bind def
/col229 {0.286 0.286 0.286 srgb} bind def
/col230 {0.843 0.843 0.843 srgb} bind def
/col231 {0.557 0.557 0.651 srgb} bind def
/col232 {0.557 0.412 0.412 srgb} bind def
/col233 {0.349 0.349 0.349 srgb} bind def
/col234 {0.380 0.380 0.380 srgb} bind def
/col235 {0.557 0.620 0.412 srgb} bind def
/col236 {0.969 0.412 0.000 srgb} bind def
/col237 {0.557 0.620 0.475 srgb} bind def
/col238 {0.286 0.286 0.286 srgb} bind def
/col239 {0.094 0.286 0.094 srgb} bind def
/col240 {0.349 0.412 0.220 srgb} bind def
/col241 {0.843 0.843 0.843 srgb} bind def
/col242 {0.682 0.682 0.682 srgb} bind def
/col243 {0.557 0.557 0.651 srgb} bind def
/col244 {0.969 0.745 0.349 srgb} bind def
/col245 {0.557 0.620 0.412 srgb} bind def
/col246 {0.286 0.286 0.286 srgb} bind def
/col247 {0.380 0.380 0.380 srgb} bind def
/col248 {0.380 0.412 0.620 srgb} bind def
/col249 {0.557 0.412 0.412 srgb} bind def
/col250 {0.969 0.969 0.969 srgb} bind def
/col251 {0.875 0.000 0.000 srgb} bind def
/col252 {0.349 0.349 0.349 srgb} bind def
/col253 {0.557 0.620 0.412 srgb} bind def
/col254 {0.286 0.286 0.286 srgb} bind def
/col255 {0.380 0.380 0.380 srgb} bind def
/col256 {0.349 0.412 0.220 srgb} bind def
/col257 {0.843 0.843 0.843 srgb} bind def
/col258 {0.682 0.682 0.682 srgb} bind def
/col259 {0.557 0.557 0.651 srgb} bind def
/col260 {0.969 0.745 0.349 srgb} bind def
/col261 {0.557 0.620 0.412 srgb} bind def
/col262 {0.286 0.286 0.286 srgb} bind def
/col263 {0.380 0.380 0.380 srgb} bind def
/col264 {0.349 0.412 0.220 srgb} bind def
/col265 {0.843 0.843 0.843 srgb} bind def
/col266 {0.682 0.682 0.682 srgb} bind def
/col267 {0.557 0.557 0.651 srgb} bind def
/col268 {0.969 0.745 0.349 srgb} bind def
/col269 {0.557 0.620 0.412 srgb} bind def
/col270 {0.286 0.286 0.286 srgb} bind def
/col271 {0.380 0.380 0.380 srgb} bind def
/col272 {0.380 0.412 0.620 srgb} bind def
/col273 {0.318 0.412 0.157 srgb} bind def
/col274 {0.380 0.380 0.380 srgb} bind def
/col275 {0.349 0.412 0.220 srgb} bind def
/col276 {0.588 0.588 0.588 srgb} bind def
/col277 {0.380 0.380 0.380 srgb} bind def
/col278 {0.000 0.380 0.000 srgb} bind def
/col279 {0.557 0.557 0.651 srgb} bind def
/col280 {0.557 0.557 0.651 srgb} bind def
/col281 {0.557 0.557 0.651 srgb} bind def
/col282 {0.000 0.380 0.286 srgb} bind def
/col283 {0.475 0.525 0.286 srgb} bind def
/col284 {0.906 0.745 0.475 srgb} bind def
/col285 {0.557 0.620 0.475 srgb} bind def
/col286 {0.651 0.714 0.780 srgb} bind def
/col287 {0.412 0.412 0.588 srgb} bind def
/col288 {0.525 0.412 0.412 srgb} bind def
/col289 {0.318 0.620 0.286 srgb} bind def
/col290 {0.843 0.906 0.906 srgb} bind def
/col291 {0.318 0.380 0.380 srgb} bind def
/col292 {0.094 0.412 0.286 srgb} bind def
/col293 {0.620 0.651 0.714 srgb} bind def
/col294 {1.000 0.588 0.000 srgb} bind def
/col295 {1.000 0.588 0.000 srgb} bind def
/col296 {0.557 0.412 0.412 srgb} bind def
/col297 {0.000 0.380 0.286 srgb} bind def
/col298 {0.475 0.525 0.286 srgb} bind def
/col299 {0.380 0.443 0.475 srgb} bind def
/col300 {0.906 0.745 0.475 srgb} bind def
/col301 {0.094 0.286 0.094 srgb} bind def
/col302 {0.349 0.412 0.220 srgb} bind def
/col303 {0.557 0.557 0.651 srgb} bind def
/col304 {0.969 0.745 0.349 srgb} bind def
/col305 {0.557 0.620 0.412 srgb} bind def
/col306 {0.286 0.286 0.286 srgb} bind def
/col307 {0.380 0.380 0.380 srgb} bind def
/col308 {0.843 0.843 0.843 srgb} bind def
/col309 {0.682 0.682 0.682 srgb} bind def
/col310 {0.557 0.557 0.651 srgb} bind def
/col311 {0.286 0.286 0.286 srgb} bind def
/col312 {0.380 0.380 0.380 srgb} bind def
/col313 {0.557 0.412 0.412 srgb} bind def
/col314 {0.349 0.349 0.349 srgb} bind def
/col315 {0.286 0.286 0.286 srgb} bind def
/col316 {0.380 0.380 0.380 srgb} bind def
/col317 {0.682 0.682 0.682 srgb} bind def
/col318 {0.380 0.380 0.380 srgb} bind def
/col319 {0.557 0.620 0.412 srgb} bind def
/col320 {0.286 0.286 0.286 srgb} bind def
/col321 {0.349 0.412 0.220 srgb} bind def
/col322 {0.682 0.682 0.682 srgb} bind def
/col323 {0.286 0.286 0.286 srgb} bind def
/col324 {0.000 0.396 0.000 srgb} bind def
/col325 {0.349 0.412 0.220 srgb} bind def
/col326 {0.812 0.827 0.812 srgb} bind def
/col327 {0.682 0.667 0.682 srgb} bind def
/col328 {0.557 0.557 0.651 srgb} bind def
/col329 {0.937 0.729 0.349 srgb} bind def
/col330 {0.557 0.604 0.412 srgb} bind def
/col331 {0.286 0.286 0.286 srgb} bind def
/col332 {0.380 0.396 0.380 srgb} bind def
/col333 {0.843 0.843 0.843 srgb} bind def
/col334 {0.557 0.557 0.651 srgb} bind def
/col335 {0.349 0.349 0.349 srgb} bind def
/col336 {0.380 0.380 0.380 srgb} bind def
/col337 {0.843 0.843 0.843 srgb} bind def
/col338 {0.349 0.412 0.220 srgb} bind def
/col339 {0.557 0.557 0.651 srgb} bind def
/col340 {0.557 0.412 0.412 srgb} bind def
/col341 {0.349 0.349 0.349 srgb} bind def
/col342 {0.380 0.380 0.380 srgb} bind def
/col343 {0.557 0.620 0.412 srgb} bind def
/col344 {0.286 0.286 0.286 srgb} bind def
/col345 {0.843 0.843 0.843 srgb} bind def
/col346 {0.557 0.557 0.651 srgb} bind def
/col347 {0.557 0.412 0.412 srgb} bind def
/col348 {0.349 0.349 0.349 srgb} bind def
/col349 {0.380 0.380 0.380 srgb} bind def
/col350 {0.557 0.620 0.475 srgb} bind def
/col351 {0.286 0.286 0.286 srgb} bind def
/col352 {0.000 0.380 0.000 srgb} bind def
/col353 {0.349 0.412 0.220 srgb} bind def
/col354 {0.875 0.875 0.875 srgb} bind def
/col355 {0.682 0.682 0.682 srgb} bind def
/col356 {0.557 0.557 0.651 srgb} bind def
/col357 {0.969 0.745 0.349 srgb} bind def
/col358 {0.557 0.620 0.412 srgb} bind def
/col359 {0.286 0.286 0.286 srgb} bind def
/col360 {0.380 0.380 0.380 srgb} bind def
/col361 {0.380 0.412 0.620 srgb} bind def
/col362 {0.843 0.843 0.843 srgb} bind def
/col363 {0.557 0.412 0.412 srgb} bind def
/col364 {0.349 0.349 0.349 srgb} bind def
/col365 {0.000 0.396 0.000 srgb} bind def
/col366 {0.349 0.412 0.220 srgb} bind def
/col367 {0.812 0.827 0.812 srgb} bind def
/col368 {0.682 0.667 0.682 srgb} bind def
/col369 {0.557 0.557 0.651 srgb} bind def
/col370 {0.937 0.729 0.349 srgb} bind def
/col371 {0.557 0.604 0.412 srgb} bind def
/col372 {0.286 0.286 0.286 srgb} bind def
/col373 {0.380 0.396 0.380 srgb} bind def
/col374 {0.349 0.412 0.220 srgb} bind def
/col375 {0.812 0.827 0.812 srgb} bind def
/col376 {0.682 0.667 0.682 srgb} bind def
/col377 {0.557 0.557 0.651 srgb} bind def
/col378 {0.937 0.729 0.349 srgb} bind def
/col379 {0.557 0.604 0.412 srgb} bind def
/col380 {0.286 0.286 0.286 srgb} bind def
/col381 {0.380 0.396 0.380 srgb} bind def
/col382 {0.349 0.412 0.220 srgb} bind def
/col383 {0.812 0.827 0.812 srgb} bind def
/col384 {0.682 0.667 0.682 srgb} bind def
/col385 {0.557 0.557 0.651 srgb} bind def
/col386 {0.937 0.729 0.349 srgb} bind def
/col387 {0.557 0.604 0.412 srgb} bind def
/col388 {0.286 0.286 0.286 srgb} bind def
/col389 {0.380 0.396 0.380 srgb} bind def
/col390 {0.349 0.412 0.220 srgb} bind def
/col391 {0.812 0.827 0.812 srgb} bind def
/col392 {0.682 0.667 0.682 srgb} bind def
/col393 {0.557 0.557 0.651 srgb} bind def
/col394 {0.937 0.729 0.349 srgb} bind def
/col395 {0.557 0.604 0.412 srgb} bind def
/col396 {0.286 0.286 0.286 srgb} bind def
/col397 {0.380 0.396 0.380 srgb} bind def
/col398 {0.349 0.412 0.220 srgb} bind def
/col399 {0.812 0.827 0.812 srgb} bind def
/col400 {0.682 0.667 0.682 srgb} bind def
/col401 {0.557 0.557 0.651 srgb} bind def
/col402 {0.937 0.729 0.349 srgb} bind def
/col403 {0.557 0.604 0.412 srgb} bind def
/col404 {0.286 0.286 0.286 srgb} bind def
/col405 {0.380 0.396 0.380 srgb} bind def
/col406 {0.843 0.843 0.843 srgb} bind def
/col407 {0.557 0.557 0.651 srgb} bind def
/col408 {0.349 0.349 0.349 srgb} bind def
/col409 {0.380 0.380 0.380 srgb} bind def
/col410 {0.000 0.396 0.000 srgb} bind def
/col411 {0.349 0.412 0.220 srgb} bind def
/col412 {0.812 0.827 0.812 srgb} bind def
/col413 {0.682 0.667 0.682 srgb} bind def
/col414 {0.557 0.557 0.651 srgb} bind def
/col415 {0.937 0.729 0.349 srgb} bind def
/col416 {0.557 0.604 0.412 srgb} bind def
/col417 {0.286 0.286 0.286 srgb} bind def
/col418 {0.380 0.396 0.380 srgb} bind def
/col419 {0.349 0.412 0.220 srgb} bind def
/col420 {0.812 0.827 0.812 srgb} bind def
/col421 {0.682 0.667 0.682 srgb} bind def
/col422 {0.557 0.557 0.651 srgb} bind def
/col423 {0.937 0.729 0.349 srgb} bind def
/col424 {0.557 0.604 0.412 srgb} bind def
/col425 {0.286 0.286 0.286 srgb} bind def
/col426 {0.380 0.396 0.380 srgb} bind def
/col427 {0.349 0.412 0.220 srgb} bind def
/col428 {0.812 0.827 0.812 srgb} bind def
/col429 {0.682 0.667 0.682 srgb} bind def
/col430 {0.557 0.557 0.651 srgb} bind def
/col431 {0.937 0.729 0.349 srgb} bind def
/col432 {0.557 0.604 0.412 srgb} bind def
/col433 {0.286 0.286 0.286 srgb} bind def
/col434 {0.380 0.396 0.380 srgb} bind def
/col435 {0.349 0.412 0.220 srgb} bind def
/col436 {0.812 0.827 0.812 srgb} bind def
/col437 {0.682 0.667 0.682 srgb} bind def
/col438 {0.557 0.557 0.651 srgb} bind def
/col439 {0.937 0.729 0.349 srgb} bind def
/col440 {0.557 0.604 0.412 srgb} bind def
/col441 {0.286 0.286 0.286 srgb} bind def
/col442 {0.380 0.396 0.380 srgb} bind def
/col443 {0.843 0.843 0.843 srgb} bind def
/col444 {0.557 0.557 0.651 srgb} bind def
/col445 {0.349 0.349 0.349 srgb} bind def
/col446 {0.380 0.380 0.380 srgb} bind def
/col447 {0.937 0.937 0.812 srgb} bind def
/col448 {0.969 0.682 0.349 srgb} bind def
/col449 {0.588 0.812 0.620 srgb} bind def
/col450 {0.682 0.667 0.682 srgb} bind def
/col451 {0.714 0.078 0.475 srgb} bind def
/col452 {0.937 0.937 0.937 srgb} bind def
/col453 {0.525 0.525 0.525 srgb} bind def
/col454 {0.000 0.380 0.000 srgb} bind def
/col455 {0.349 0.412 0.220 srgb} bind def
/col456 {0.843 0.843 0.843 srgb} bind def
/col457 {0.682 0.682 0.682 srgb} bind def
/col458 {0.557 0.557 0.651 srgb} bind def
/col459 {0.969 0.745 0.349 srgb} bind def
/col460 {0.557 0.620 0.412 srgb} bind def
/col461 {0.286 0.286 0.286 srgb} bind def
/col462 {0.380 0.380 0.380 srgb} bind def
/col463 {0.380 0.412 0.620 srgb} bind def
/col464 {0.475 0.475 0.475 srgb} bind def
/col465 {0.000 0.349 0.000 srgb} bind def
/col466 {0.906 0.443 0.443 srgb} bind def
/col467 {0.875 0.000 0.000 srgb} bind def
/col468 {1.000 0.796 0.188 srgb} bind def
/col469 {0.157 0.475 0.286 srgb} bind def
/col470 {0.875 0.157 0.125 srgb} bind def
/col471 {0.125 0.349 0.780 srgb} bind def
/col472 {0.969 0.984 0.969 srgb} bind def
/col473 {0.937 0.937 0.937 srgb} bind def
/col474 {0.906 0.906 0.906 srgb} bind def
/col475 {0.000 0.380 0.286 srgb} bind def
/col476 {0.475 0.525 0.286 srgb} bind def
/col477 {0.843 0.843 0.843 srgb} bind def
/col478 {0.682 0.682 0.682 srgb} bind def
/col479 {0.380 0.443 0.475 srgb} bind def
/col480 {0.906 0.745 0.475 srgb} bind def
/col481 {0.557 0.620 0.475 srgb} bind def
/col482 {0.286 0.286 0.286 srgb} bind def
/col483 {0.651 0.714 0.780 srgb} bind def
/col484 {0.412 0.412 0.588 srgb} bind def
/col485 {0.525 0.412 0.412 srgb} bind def
/col486 {0.318 0.620 0.286 srgb} bind def
/col487 {0.843 0.906 0.906 srgb} bind def
/col488 {0.318 0.380 0.380 srgb} bind def
/col489 {0.094 0.412 0.286 srgb} bind def
/col490 {0.620 0.651 0.714 srgb} bind def
/col491 {0.125 0.525 0.349 srgb} bind def
/col492 {0.000 0.380 0.000 srgb} bind def
/col493 {0.349 0.412 0.220 srgb} bind def
/col494 {0.557 0.557 0.651 srgb} bind def
/col495 {0.969 0.745 0.349 srgb} bind def
/col496 {0.557 0.620 0.412 srgb} bind def
/col497 {0.380 0.380 0.380 srgb} bind def
/col498 {0.380 0.412 0.620 srgb} bind def
/col499 {0.380 0.380 0.380 srgb} bind def
/col500 {0.349 0.412 0.220 srgb} bind def
/col501 {0.843 0.843 0.843 srgb} bind def
/col502 {0.682 0.682 0.682 srgb} bind def
/col503 {0.557 0.557 0.651 srgb} bind def
/col504 {0.969 0.745 0.349 srgb} bind def
/col505 {0.557 0.620 0.412 srgb} bind def
/col506 {0.286 0.286 0.286 srgb} bind def
/col507 {0.380 0.380 0.380 srgb} bind def
/col508 {0.557 0.412 0.412 srgb} bind def
/col509 {0.349 0.349 0.349 srgb} bind def
/col510 {0.812 0.812 0.812 srgb} bind def
/col511 {0.255 0.271 0.255 srgb} bind def
/col512 {0.525 0.510 0.525 srgb} bind def
/col513 {0.745 0.765 0.745 srgb} bind def
/col514 {0.745 0.765 0.745 srgb} bind def
/col515 {0.525 0.510 0.525 srgb} bind def
/col516 {0.525 0.510 0.525 srgb} bind def
/col517 {0.745 0.765 0.745 srgb} bind def
/col518 {0.620 0.000 0.000 srgb} bind def
/col519 {0.620 0.000 0.000 srgb} bind def
/col520 {0.557 0.557 0.557 srgb} bind def
/col521 {0.255 0.255 0.255 srgb} bind def
/col522 {0.557 0.557 0.557 srgb} bind def
/col523 {0.255 0.255 0.255 srgb} bind def
/col524 {0.557 0.557 0.557 srgb} bind def
/col525 {0.255 0.255 0.255 srgb} bind def
/col526 {0.557 0.557 0.557 srgb} bind def
/col527 {0.255 0.255 0.255 srgb} bind def
/col528 {0.557 0.557 0.557 srgb} bind def
/col529 {0.255 0.255 0.255 srgb} bind def
/col530 {0.557 0.557 0.557 srgb} bind def
/col531 {0.255 0.255 0.255 srgb} bind def
/col532 {0.620 0.000 0.000 srgb} bind def
/col533 {0.620 0.000 0.000 srgb} bind def
/col534 {0.745 0.765 0.745 srgb} bind def
/col535 {0.412 0.427 0.412 srgb} bind def
/col536 {0.745 0.765 0.745 srgb} bind def
/col537 {0.412 0.427 0.412 srgb} bind def
/col538 {0.286 0.271 0.286 srgb} bind def
/col539 {0.557 0.557 0.557 srgb} bind def
/col540 {0.412 0.427 0.412 srgb} bind def
/col541 {0.557 0.557 0.557 srgb} bind def
/col542 {0.745 0.765 0.745 srgb} bind def

end
save
newpath 0 192 moveto 0 0 lineto 403 0 lineto 403 192 lineto closepath clip newpath
-36.0 208.0 translate
1 -1 scale

/cp {closepath} bind def
/ef {eofill} bind def
/gr {grestore} bind def
/gs {gsave} bind def
/sa {save} bind def
/rs {restore} bind def
/l {lineto} bind def
/m {moveto} bind def
/rm {rmoveto} bind def
/n {newpath} bind def
/s {stroke} bind def
/sh {show} bind def
/slc {setlinecap} bind def
/slj {setlinejoin} bind def
/slw {setlinewidth} bind def
/srgb {setrgbcolor} bind def
/rot {rotate} bind def
/sc {scale} bind def
/sd {setdash} bind def
/ff {findfont} bind def
/sf {setfont} bind def
/scf {scalefont} bind def
/sw {stringwidth} bind def
/tr {translate} bind def
/tnt {dup dup currentrgbcolor
  4 -2 roll dup 1 exch sub 3 -1 roll mul add
  4 -2 roll dup 1 exch sub 3 -1 roll mul add
  4 -2 roll dup 1 exch sub 3 -1 roll mul add srgb}
  bind def
/shd {dup dup currentrgbcolor 4 -2 roll mul 4 -2 roll mul
  4 -2 roll mul srgb} bind def
 /DrawEllipse {
	/endangle exch def
	/startangle exch def
	/yrad exch def
	/xrad exch def
	/y exch def
	/x exch def
	/savematrix mtrx currentmatrix def
	x y tr xrad yrad sc 0 0 1 startangle endangle arc
	closepath
	savematrix setmatrix
	} def

/$F2psBegin {$F2psDict begin /$F2psEnteredState save def} def
/$F2psEnd {$F2psEnteredState restore end} def

$F2psBegin
%%Page: 1 1
10 setmiterlimit
 0.06000 0.06000 sc
%
% Fig objects follow
%
/Times-Italic ff 210.00 scf sf
620 2282 m
gs 1 -1 sc (x) col0 sh gr
/Times-Italic ff 150.00 scf sf
740 2342 m
gs 1 -1 sc (1) col0 sh gr
/Times-Italic ff 240.00 scf sf
2337 3393 m
gs 1 -1 sc (z) col0 sh gr
/Times-Italic ff 150.00 scf sf
2470 3460 m
gs 1 -1 sc (2) col0 sh gr
/Times-Italic ff 240.00 scf sf
1872 3393 m
gs 1 -1 sc (z) col0 sh gr
/Times-Italic ff 150.00 scf sf
2005 3460 m
gs 1 -1 sc (1) col0 sh gr
/Times-Italic ff 240.00 scf sf
2064 413 m
gs 1 -1 sc (z) col0 sh gr
/Times-Italic ff 150.00 scf sf
2196 478 m
gs 1 -1 sc (3) col0 sh gr
/Times-Italic ff 240.00 scf sf
5655 3395 m
gs 1 -1 sc (z) col0 sh gr
/Times-Italic ff 150.00 scf sf
5787 3460 m
gs 1 -1 sc (3) col0 sh gr
/Times-Italic ff 210.00 scf sf
5395 430 m
gs 1 -1 sc (x) col0 sh gr
/Times-Italic ff 150.00 scf sf
5515 490 m
gs 1 -1 sc (2) col0 sh gr
/Times-Italic ff 210.00 scf sf
5927 430 m
gs 1 -1 sc (y) col0 sh gr
/Times-Italic ff 150.00 scf sf
6047 490 m
gs 1 -1 sc (2) col0 sh gr
/Times-Italic ff 210.00 scf sf
4502 2882 m
gs 1 -1 sc (x) col0 sh gr
/Times-Italic ff 150.00 scf sf
4622 2942 m
gs 1 -1 sc (1) col0 sh gr
/Times-Italic ff 210.00 scf sf
6910 2882 m
gs 1 -1 sc (y) col0 sh gr
/Times-Italic ff 150.00 scf sf
7030 2942 m
gs 1 -1 sc (3) col0 sh gr
/Times-Italic ff 210.00 scf sf
4255 2507 m
gs 1 -1 sc (y) col0 sh gr
/Times-Italic ff 150.00 scf sf
4375 2567 m
gs 1 -1 sc (1) col0 sh gr
/Times-Italic ff 210.00 scf sf
7112 2507 m
gs 1 -1 sc (x) col0 sh gr
/Times-Italic ff 150.00 scf sf
7232 2567 m
gs 1 -1 sc (3) col0 sh gr
% Polyline
7.500 slw
n 5772 1829 m
 5772 1949 l gs col0 s gr 
% Polyline
n 5712 1889 m
 5832 1889 l gs col0 s gr 
% Polyline
n 2155 1825 m
 2155 1945 l gs col0 s gr 
% Polyline
n 2095 1885 m
 2215 1885 l gs col0 s gr 
/Times-Italic ff 210.00 scf sf
1552 503 m
gs 1 -1 sc (x) col0 sh gr
/Times-Italic ff 150.00 scf sf
1672 563 m
gs 1 -1 sc (3) col0 sh gr
/Times-Italic ff 210.00 scf sf
3525 1485 m
gs 1 -1 sc (x) col0 sh gr
/Times-Italic ff 150.00 scf sf
3645 1545 m
gs 1 -1 sc (2) col0 sh gr
/Times-Italic ff 210.00 scf sf
607 1470 m
gs 1 -1 sc (y) col0 sh gr
/Times-Italic ff 150.00 scf sf
727 1530 m
gs 1 -1 sc (2) col0 sh gr
/Times-Italic ff 210.00 scf sf
3447 2439 m
gs 1 -1 sc (y) col0 sh gr
/Times-Italic ff 150.00 scf sf
3567 2499 m
gs 1 -1 sc (1) col0 sh gr
/Times-Italic ff 210.00 scf sf
2557 510 m
gs 1 -1 sc (y) col0 sh gr
/Times-Italic ff 150.00 scf sf
2677 570 m
gs 1 -1 sc (3) col0 sh gr
/Times-Italic ff 240.00 scf sf
4320 1090 m
gs 1 -1 sc (z) col0 sh gr
/Times-Italic ff 150.00 scf sf
4453 1157 m
gs 1 -1 sc (1) col0 sh gr
/Times-Italic ff 240.00 scf sf
7012 1089 m
gs 1 -1 sc (z) col0 sh gr
/Times-Italic ff 150.00 scf sf
7145 1156 m
gs 1 -1 sc (2) col0 sh gr
15.000 slw
% Ellipse
n 2151 1883 1224 1224 0 360 DrawEllipse gs col0 s gr

% Rotated Ellipse
gs
5771 1882 tr
-180.000 rot
n 0 0 1224 1224 0 360 DrawEllipse 180.000 rot
gs col0 s gr
gr

% Polyline
7.500 slw
 [15 60] 60 sd
n 1008 2275 m 3364 1680 l 1939 671 l
 cp gs col0 s gr  [] 0 sd
% Polyline
 [15 60] 60 sd
n 6743 2634 m 4638 2343 l 5940 674 l
 cp gs col0 s gr  [] 0 sd
% Polyline
 [15 60] 60 sd
n 4824 2634 m 6906 2343 l 5609 679 l
 cp gs col0 s gr  [] 0 sd
% Polyline
 [15 45] 45 sd
n 4709 1274 m 6826 1271 l 5772 3093 l
 cp gs col0 s gr  [] 0 sd
% Polyline
 [15 45] 45 sd
n 2044 3100 m 2278 3100 l 2150 658 l
 cp gs col0 s gr  [] 0 sd
/Times-Bold ff 210.00 scf sf
5618 1740 m
gs 1 -1 sc (0) col0 sh gr
/Times-Bold ff 210.00 scf sf
1961 1876 m
gs 1 -1 sc (0) col0 sh gr
% Polyline
 [15 60] 60 sd
n 2380 670 m 946 1658 l 3297 2258 l
 cp gs col0 s gr  [] 0 sd
% Polyline
n 1875 728 m 1995 728 l 1995 608 l 1875 608 l
 cp gs col7 1.00 shd ef gr gs col0 s gr 
% Polyline
n 2078 658 m 2152 584 l 2226 658 l 2152 732 l
 cp gs col7 1.00 shd ef gr gs col0 s gr 
% Polyline
n 1971 3101 m 2045 3027 l 2119 3101 l 2045 3175 l
 cp gs col7 1.00 shd ef gr gs col0 s gr 
% Polyline
n 5696 3091 m 5770 3017 l 5844 3091 l 5770 3165 l
 cp gs col7 1.00 shd ef gr gs col0 s gr 
% Polyline
n 4636 1271 m 4710 1197 l 4784 1271 l 4710 1345 l
 cp gs col7 1.00 shd ef gr gs col0 s gr 
% Polyline
n 6752 1270 m 6826 1196 l 6900 1270 l 6826 1344 l
 cp gs col7 1.00 shd ef gr gs col0 s gr 
% Polyline
n 5545 735 m 5665 735 l 5665 615 l 5545 615 l
 cp gs col7 1.00 shd ef gr gs col0 s gr 
% Polyline
n 4760 2690 m 4880 2690 l 4880 2570 l 4760 2570 l
 cp gs col7 1.00 shd ef gr gs col0 s gr 
% Polyline
n 6844 2402 m 6964 2402 l 6964 2282 l 6844 2282 l
 cp gs col7 1.00 shd ef gr gs col0 s gr 
% Ellipse
n 945 1658 65 65 0 360 DrawEllipse gs col7 1.00 shd ef gr gs col0 s gr

% Ellipse
n 2385 668 65 65 0 360 DrawEllipse gs col7 1.00 shd ef gr gs col0 s gr

% Ellipse
n 3300 2258 65 65 0 360 DrawEllipse gs col7 1.00 shd ef gr gs col0 s gr

% Ellipse
n 5940 675 65 65 0 360 DrawEllipse gs col7 1.00 shd ef gr gs col0 s gr

% Ellipse
n 4635 2336 65 65 0 360 DrawEllipse gs col7 1.00 shd ef gr gs col0 s gr

% Ellipse
n 6742 2631 65 65 0 360 DrawEllipse gs col7 1.00 shd ef gr gs col0 s gr

% Polyline
n 945 2333 m 1065 2333 l 1065 2213 l 945 2213 l
 cp gs col7 1.00 shd ef gr gs col0 s gr 
% Polyline
n 3300 1733 m 3420 1733 l 3420 1613 l 3300 1613 l
 cp gs col7 1.00 shd ef gr gs col0 s gr 
% Polyline
n 2204 3101 m 2278 3027 l 2352 3101 l 2278 3175 l
 cp gs col7 1.00 shd ef gr gs col0 s gr 
$F2psEnd
rs

%%EndDocument
 @endspecial 411 2829 a Ft(Figure)38 b(5.)48 b Fu(The)34
b(t)m(w)m(o)f(con\014gurations)g(in)g(dimension)h(2)f(with)g
FA(depth)3100 2852 y Fh(S)3150 2829 y Fu(\()p FA(0)p
Fu(\))27 b(=)h(9.)100 3043 y(W)-8 b(e)28 b(can)f(build)i(a)e
(con\014guration)h FA(S)1405 3007 y Fo(+)1492 3043 y
Fu(with)g FA(depth)1990 3067 y Fh(S)2035 3048 y Fg(+)2090
3043 y Fu(\()p FA(0)p Fu(\))g(=)g Fs(d)2405 3007 y Fq(d)p
Fo(+1)2547 3043 y Fu(+)12 b(1)27 b(b)m(y)h(follo)m(wing)g(the)g
(strategy)g(for)0 3159 y FA(S)62 3123 y Fj(\000)152 3159
y Fu(but)k(building)f(a)g(deep)h(cell)g(rather)f(than)g(a)g(shallo)m(w)
h(one.)43 b(T)-8 b(o)31 b(do)g(this,)h(w)m(e)g(place)g(the)f(p)s(olar)g
(region)0 3275 y(p)s(oin)m(ts)37 b(of)e(colour)i Fs(i)f
Fu(close)h(to)f(the)g(geo)s(desic)i(b)s(et)m(w)m(een)g
Fs(p)2124 3290 y Fo(north)2333 3275 y Fu(and)e(the)g(p)s(oin)m(t)h(of)e
(colour)h Fs(i)h Fu(on)f(Cancer.)0 3392 y(Then)k Fs(p)310
3407 y Fo(north)523 3392 y Fu(is)f(con)m(tained)i(in)e(ev)m(ery)j
(colourful)d(cone)h(generated)g(b)m(y)h(p)s(oin)m(ts)f(from)f(Cancer)h
(and)g(the)0 3508 y(p)s(olar)29 b(region)g(\(in)g(fact)h(these)g(are)f
(all)h(the)f(colourful)h(cones)g(con)m(taining)g Fs(p)2756
3523 y Fo(north)2929 3508 y Fu(\).)42 b(Hence)31 b(the)e(cell)h
Fs(C)3727 3523 y Fo(north)0 3624 y Fu(con)m(taining)g
Fs(p)520 3639 y Fo(north)722 3624 y Fu(has)f(depth)h
Fs(d)1216 3588 y Fq(d)1256 3624 y Fu(.)43 b(By)29 b(placing)h(the)g(p)s
(oin)m(ts)f(of)g Fs(S)2436 3583 y Fo(+)2430 3652 y Fq(d)p
Fo(+1)2590 3624 y Fu(so)g(that)g Fs(d)g Fu(of)f(their)i(an)m(tip)s(o)s
(des)g(are)0 3749 y(in)37 b Fs(C)188 3764 y Fo(north)397
3749 y Fu(and)f(the)h(\014nal)g(an)m(tip)s(o)s(de)f(is)h(at)f
Fs(p)1664 3764 y Fo(south)1837 3749 y Fu(,)i(w)m(e)f(get)f
FA(S)2277 3713 y Fo(+)2373 3749 y Fu(with)h FA(depth)2881
3773 y Fh(S)2926 3754 y Fg(+)2981 3749 y Fu(\()p FA(0)p
Fu(\))d(=)g Fs(d)24 b Fn(\001)h Fs(d)3436 3713 y Fq(d)3501
3749 y Fu(+)f(1.)55 b(The)0 3866 y(t)m(w)m(o-dimensional)34
b FA(S)783 3830 y Fo(+)875 3866 y Fu(app)s(ears)f(as)g(the)g(left)g
(elemen)m(t)h(of)e(Figure)h(5.)100 3982 y(A)24 b(more)h(symmetric)i
(\(but)e(similar\))h(construction)g(places)g(one)f(p)s(oin)m(t)f(of)h
(eac)m(h)g(colour)g(at)g(the)g(v)m(ertices)0 4098 y(of)32
b(a)g(regular)h(simplex,)i(and)d(the)h(remaining)h(p)s(oin)m(ts)f
(surround)g(the)g(an)m(tip)s(o)s(de)g(of)f(the)h(same)g(colour.)100
4214 y(It)h(follo)m(ws)g(that)g Fs(\027)6 b Fu(\()p Fs(d)p
Fu(\))30 b Fn(\025)g Fs(d)1110 4178 y Fq(d)p Fo(+1)1264
4214 y Fu(+)23 b(1.)47 b(W)-8 b(e)34 b(conjecture)h(that)f(this)g(b)s
(ound)g(is)h(tigh)m(t.)48 b(As)34 b(with)h(Conjec-)0
4331 y(ture)e(4.2)f(a)g(computer)i(searc)m(h)g(did)f(not)f(turn)h(up)g
(an)m(y)g(coun)m(terexamples.)0 4486 y FA(Conjecture)45
b(4.4.)h Fu(The)40 b(maxim)m(um)h(colourful)e(simplicial)i(depth)f(of)f
(an)m(y)h(p)s(oin)m(t)f(in)h(the)g(in)m(terior)f(of)0
4602 y(the)30 b(core)g(of)g(an)m(y)g(colourful)g(con\014guration)g(of)g
(\()p Fs(d)17 b Fu(+)g(1\))28 b(p)s(oin)m(ts)i(in)g(eac)m(h)h(of)e(\()p
Fs(d)17 b Fu(+)g(1\))28 b(colours)j(is)f Fs(d)3585 4566
y Fq(d)p Fo(+1)3732 4602 y Fu(+)17 b(1.)0 4718 y(That)33
b(is,)g(w)m(e)h(ha)m(v)m(e)g Fs(\027)6 b Fu(\()p Fs(d)p
Fu(\))27 b(=)h Fs(d)1101 4682 y Fq(d)p Fo(+1)1253 4718
y Fu(+)22 b(1.)0 4873 y Fp(R)-5 b(emark)45 b Fu(4.5)p
Fp(.)40 b Fu(F)-8 b(or)32 b(an)m(y)h Fs(d)p Fu(,)f(there)h(exists)h(a)e
(colourful)g(con\014guration)g FA(S)h Fu(whic)m(h)h(con)m(tains)f
FA(0)f Fu(in)g(at)g(least)0 4990 y(32\045)g(of)g(its)h(colourful)g
(simplices.)100 5145 y(A)g(con\014guration)g(of)g(\()p
Fs(d)22 b Fu(+)g(1\))33 b(p)s(oin)m(ts)h(in)g(eac)m(h)g(of)e(\()p
Fs(d)22 b Fu(+)h(1\))33 b(colours)g(generates)i(\()p
Fs(d)22 b Fu(+)g(1\))3365 5108 y Fq(d)p Fo(+1)3529 5145
y Fu(colourful)0 5261 y(simplices,)42 b(so)c(Remark)g(4.5)g(follo)m(ws)
g(immediately)i(from)e(the)g(construction)h(of)f FA(S)3145
5225 y Fo(+)3204 5261 y Fu(.)59 b(The)39 b(minim)m(um)p
eop end
%%Page: 16 16
TeXDict begin 16 15 bop 0 75 a Fl(16)498 b(ANTOINE)25
b(DEZA,)g(SUI)f(HUANG,)h(T)-6 b(AMON)25 b(STEPHEN)h(AND)e(T)-6
b(AM)2823 56 y(\023)2813 75 y(AS)25 b(TERLAKY)0 274 y
Fu(fraction)g(of)g(colourful)h(simplices)i(con)m(taining)e
FA(0)g Fu(from)f(an)g FA(S)2222 238 y Fo(+)2307 274 y
Fu(con\014guration)h(is)g(82)p Fs(=)p Fu(256)e(attained)i(when)0
390 y Fs(d)h Fu(=)h(3.)1488 628 y(5.)49 b Ft(Open)37
b(Questions)100 802 y Fu(W)-8 b(e)43 b(w)m(ould)h(lik)m(e)h(to)e
(conclude)h(b)m(y)h(men)m(tioning)f(that)f(there)h(are)f(man)m(y)h
(more)g(natural)f(questions)0 919 y(relating)33 b(to)f(colourful)h(and)
f(mono)s(c)m(hrome)i(simplicial)g(depth.)44 b(The)34
b(\014rst)f(is:)0 1101 y FA(Question)49 b(5.1.)d Fu(What)c(is)g(a)f(t)m
(ypical)i(v)-5 b(alue)42 b(of)f(m\()p FA(S)p Fu(\))h(for)f(a)g(random)h
(con\014guration)f FA(S)h Fu(of)f(\()p Fs(d)28 b Fu(+)g(1\))0
1217 y(p)s(oin)m(ts)33 b(in)g(eac)m(h)g(of)g(\()p Fs(d)21
b Fu(+)h(1\))33 b(colours?)100 1400 y(In)42 b(Section)h(3,)i(w)m(e)e
(remark)m(ed)h(that)e(suc)m(h)h(random)g(con\014gurations)f(could)h(b)s
(e)g(exp)s(ected)h(to)e(ha)m(v)m(e)0 1516 y(a)k(simplicial)i(depth)f
(on)f(the)h(order)f(of)1585 1477 y Fo(1)p 1567 1493 72
4 v 1567 1551 a(2)1602 1532 y Fi(d)1648 1516 y Fu(\()p
Fs(d)32 b Fu(+)f(1\))1963 1480 y Fq(d)p Fo(+1)2139 1516
y Fu(at)46 b(the)h(origin.)85 b(W)-8 b(e)46 b(also)h(ga)m(v)m(e)g(a)f
(colourful)0 1641 y(con\014guration)36 b FA(S)656 1605
y Fj(4)759 1641 y Fu(that)g(has)g(m)q(\()p FA(S)1333
1605 y Fj(4)1400 1641 y Fu(\))d(=)g(\()p Fs(d)24 b Fu(+)h(1\)!.)53
b(Ho)m(w)m(ev)m(er,)39 b FA(S)2474 1605 y Fj(4)2577 1641
y Fu(is)e(not)f(in)g(general)g(p)s(osition.)54 b(Our)0
1757 y(construction)41 b FA(S)628 1721 y Fj(\000)727
1757 y Fu(from)f(Section)h(3.4)e(is)i(in)f(general)g(p)s(osition)g(and)
h(has)f(a)g(lo)m(w)g(v)-5 b(alue)40 b(of)g(m\()p FA(S)3637
1721 y Fj(\000)3696 1757 y Fu(\).)66 b(It)0 1874 y(is)40
b(not)g(clear)g(if)f(this)h(b)s(eha)m(viour)h(is)f(t)m(ypical,)i(i.e.)f
(if)e(most)h(con\014gurations)g(ha)m(v)m(e)h(some)g(p)s(oin)m(t)e
Fs(p)h Fu(near)0 1990 y(the)e(edge)f(of)g(the)g(core)h(that)f(drags)g
(do)m(wn)h(m\()p FA(S)p Fu(\),)h(or)d(if)h(our)g(con\014guration)h(is)f
(statistically)i(unlik)m(ely)-8 b(.)0 2106 y(Indeed)37
b(w)m(e)f(can)g(consider)h(the)e(p)s(ossibilit)m(y)j(that)d
Fp(al)5 b(l)35 b Fu(con\014gurations)h(in)f(general)h(p)s(osition)g(ha)
m(v)m(e)g(suc)m(h)0 2222 y(a)c(p)s(oin)m(t)h(near)g(the)g(edge)g(of)f
(the)h(core.)0 2405 y FA(Question)e(5.2.)37 b Fu(What)26
b(is)g(the)h(maxim)m(um)g(v)-5 b(alue)27 b(of)e(m)q(\()p
FA(S)p Fu(\))h(for)f(a)h(colourful)g(con\014guration)g
FA(S)h Fu(of)e(\()p Fs(d)9 b Fu(+)g(1\))0 2521 y(p)s(oin)m(ts)33
b(in)g(eac)m(h)g(of)g(\()p Fs(d)21 b Fu(+)h(1\))33 b(colours?)44
b(What)32 b(if)h FA(S)f Fu(is)i(not)e(assumed)i(to)e(b)s(e)h(in)g
(general)g(p)s(osition?)100 2703 y(W)-8 b(e)39 b(observ)m(e)h(that)f
(in)g(fact)f(our)h(construction)h(of)e(a)g(colourful)h(con\014guration)
g FA(S)3181 2667 y Fj(\000)3279 2703 y Fu(with)h(m\()p
FA(S)3689 2667 y Fj(\000)3748 2703 y Fu(\))e(=)0 2820
y Fs(d)51 2783 y Fo(2)117 2820 y Fu(+)27 b(1)39 b(con)m(tains)i(p)s
(oin)m(ts)f(of)f(high)h(colourful)g(simplicial)h(depth,)h(but)e(a)m(w)m
(a)m(y)h(from)e FA(0)p Fu(.)65 b(This)41 b(leads)f(us)0
2936 y(to)i(consider)i(the)e(colourful)h(analogues)g(of)f(the)g
(functions)i Fs(f)11 b Fu(\()p Fs(S)6 b Fu(\))41 b(and)i
Fs(g)t Fu(\()p Fs(S)6 b Fu(\))41 b(of)h(Section)h(2.1.)73
b(F)-8 b(or)41 b(a)0 3052 y(colourful)33 b(con\014guration)f
FA(S)p Fu(,)h(de\014ne:)445 3223 y FA(f)10 b Fu(\()p
FA(S)p Fu(\))29 b(=)e(max)767 3293 y Fq(p)p Fj(2)p Fd(R)898
3274 y Fi(d)957 3223 y FA(depth)1239 3247 y Fh(S)1288
3223 y Fu(\()p Fs(p)p Fu(\))228 b(and)f FA(g)r Fu(\()p
FA(S)p Fu(\))28 b(=)252 b(max)2352 3286 y Fq(p)23 b Fo(in)h(general)g
(p)r(osition)2999 3223 y FA(depth)3280 3247 y Fh(S)3330
3223 y Fu(\()p Fs(p)p Fu(\))272 b(\(11\))0 3454 y(W)-8
b(e)37 b(fo)s(cus)g(on)f(the)h(case)g(where)h(w)m(e)g(ha)m(v)m(e)g(\()p
Fs(d)24 b Fu(+)h(1\))36 b(colours.)56 b(It)36 b(is)h(clear)g(that)g
(giv)m(en)g(the)g(sizes)h(of)f(the)0 3570 y(colourful)25
b(sets)h Fs(S)639 3585 y Fo(1)679 3570 y Fs(;)17 b(:)g(:)g(:)f(;)h(S)
958 3585 y Fq(d)p Fo(+1)1113 3570 y Fu(comprising)26
b FA(S)f Fu(that)g(the)h(maxim)m(um)g(of)f FA(f)10 b
Fu(\()p FA(S)p Fu(\))25 b(and)g FA(g)r Fu(\()p FA(S)p
Fu(\))g(is)h Fn(j)p Fs(S)3391 3585 y Fo(1)3430 3570 y
Fn(j)7 b(\001)g Fs(:)17 b(:)g(:)5 b Fn(\001)i(j)p Fs(S)3743
3585 y Fq(d)p Fo(+1)3872 3570 y Fn(j)0 3686 y Fu(and)37
b(is)h(attained)f(b)m(y)h(placing)g(the)f(p)s(oin)m(ts)h(of)f(eac)m(h)h
(colour)f(at)g(\(or)f(near\))i(the)f(v)m(ertices)i(of)e(a)g(simplex.)0
3803 y(If)h(w)m(e)g(restrict)h FA(S)f Fu(to)f(b)s(e)h(a)f
(con\014guration)h(of)f(\()p Fs(d)25 b Fu(+)g(1\))38
b(p)s(oin)m(ts)g(in)g(eac)m(h)g(of)f(\()p Fs(d)26 b Fu(+)f(1\))37
b(colours)h(and)g(tak)m(e)0 3919 y(the)48 b(maxim)m(um)h(o)m(v)m(er)g
(the)f(in)m(terior)g(of)f(the)h(core,)k(w)m(e)c(get)g(exactly)h(the)f
(question)h(of)e(\014nding)h Fs(\027)6 b Fu(\()p Fs(d)p
Fu(\))0 4035 y(\(Conjecture)34 b(4.4\).)43 b(W)-8 b(e)33
b(are)f(also)h(in)m(terested)i(in)d(lo)m(w)m(er)i(b)s(ounds)f(for)g
FA(f)10 b Fu(\()p FA(S)p Fu(\))33 b(and)f FA(g)r Fu(\()p
FA(S)p Fu(\).)0 4217 y FA(Question)47 b(5.3.)f Fu(F)-8
b(or)40 b Fs(d)p Fu(-dimensional)h(con\014gurations)g(consisting)g(of)f
Fs(n)h Fu(p)s(oin)m(ts)g(in)g(eac)m(h)g(of)f(\()p Fs(d)27
b Fu(+)g(1\))0 4334 y(colours,)33 b(\014nd)g(lo)m(w)m(er)h(b)s(ounds)f
(for)f FA(f)10 b Fu(\()p FA(S)p Fu(\))33 b(and)g FA(g)r
Fu(\()p FA(S)p Fu(\).)100 4516 y(In)48 b(a)g(surv)m(ey)j(pap)s(er)d(on)
h(the)f(colourful)h(Carath)m(\023)-46 b(eo)s(dory)49
b(theorem,)k(B\023)-49 b(ar\023)g(an)m(y)49 b(and)f(Onn)h([BO97a)o(])0
4632 y(men)m(tion)31 b(that)f(the)g(results)i(of)d([ABFK92])h(can)g(b)s
(e)h(applied)f(to)g(giv)m(e)h(a)f(lo)m(w)m(er)h(b)s(ound)f(for)g
FA(g)r Fu(\()p FA(S)p Fu(\))g(when)h Fs(n)0 4749 y Fu(is)i(large)g(of)f
(the)h(form:)1561 4935 y FA(g)r Fu(\()p FA(S)p Fu(\))28
b Fn(\025)g Fs(c)1932 4950 y Fq(d)1972 4794 y Fk(\022)2126
4867 y Fs(n)2046 5003 y(d)22 b Fu(+)g(1)2265 4794 y Fk(\023)3727
4935 y Fu(\(12\))0 5141 y(Unfortunately)-8 b(,)33 b(the)g(constan)m(t)g
Fs(c)1253 5156 y Fq(d)1326 5141 y Fu(is)f(doubly)i(exp)s(onen)m(tial)f
(in)g Fs(d)f Fu(so)g(the)h(b)s(ound)f(is)h(only)g(non-trivial)f(if)0
5261 y Fs(n)c Fn(\035)f Fs(e)258 5225 y Fo(4)p Fq(d)329
5201 y Fg(2)369 5261 y Fu(.)43 b(In)33 b(particular,)g(it)g(sheds)h(no)
e(ligh)m(t)h(on)g(the)g Fs(n)28 b Fu(=)f Fs(d)22 b Fu(+)g(1)32
b(case.)p eop end
%%Page: 17 17
TeXDict begin 17 16 bop 1304 71 a Fl(COLOURFUL)32 b(SIMPLICIAL)g(DEPTH)
1227 b(17)100 274 y Fu(One)37 b(can)g(also)g(get)g(a)f(lo)m(w)m(er)i(b)
s(ound)f(for)g FA(g)r Fu(\()p FA(S)p Fu(\))f(directly)i(from)f(the)g
(Colourful)g(Tv)m(erb)s(erg)i(Theorem)0 395 y([)32 370
y(\024)27 395 y(ZV92)o(],)33 b(whic)m(h)h(is)f(used)h(to)e(deriv)m(e)i
(the)f(results)h(in)f([ABFK92]:)1465 613 y FA(g)r Fu(\()p
FA(S)p Fu(\))28 b Fn(\025)1804 546 y Fu(1)p 1804 590
49 4 v 1804 682 a(4)1879 473 y Fk(\022)2043 546 y Fs(n)p
1963 590 220 4 v 1963 682 a(d)21 b Fu(+)i(1)2214 613
y(+)f(3)2361 473 y Fk(\023)3727 613 y Fu(\(13\))0 832
y(This)45 b(still)g(do)s(es)g(not)f(help)h(for)e Fs(n)48
b Fu(=)f Fs(d)30 b Fu(+)f(1,)47 b(but)e(for)e(small)i
Fs(n)f Fu(the)h(b)s(ound)f(is)h(stronger)f(than)h(\(12\))0
948 y(and)31 b(comes)g(with)g(the)g(additional)g(guaran)m(tee)g(that)f
(colourful)h(simplices)i(in)m(v)m(olv)m(ed)g(are)d(disjoin)m(t!)44
b(This)0 1064 y(suggests)34 b(that)e(there)i(is)f(m)m(uc)m(h)h(ro)s(om)
e(for)g(impro)m(v)m(emen)m(t.)0 1238 y(5.1.)49 b FA(Mono)s(c)m(hrome)43
b(Questions.)50 b Fu(The)38 b(authors)f(w)m(ould)h(also)f(lik)m(e)h(to)
f(men)m(tion)h(that)e(they)i(do)f(not)0 1355 y(kno)m(w)30
b(the)g(answ)m(ers)h(to)e(some)i(fairly)e(basic)h(questions)h(ab)s(out)
e(mono)s(c)m(hrome)h(simplicial)h(depth.)44 b(Recall)0
1471 y(the)39 b(maxim)m(um)i(closed)f(and)f(op)s(en)g(depth)h
(functions)g Fs(f)11 b Fu(\()p Fs(S)6 b Fu(\))38 b(and)h
Fs(g)t Fu(\()p Fs(S)6 b Fu(\))38 b(for)g(a)h(set)h(of)e(p)s(oin)m(ts)i
Fs(S)k Fu(in)c Fr(R)3860 1435 y Fq(d)0 1587 y Fu(de\014ned)34
b(in)f(Section)g(2.1.)0 1758 y FA(Question)40 b(5.4.)i
Fu(Are)35 b(the)f(p)s(oin)m(ts)h Fs(p)f Fu(attaining)f(the)i(maxim)m
(um)h Fs(f)11 b Fu(\()p Fs(S)6 b Fu(\))33 b(in)h(\(1\))g(alw)m(a)m(ys)h
(limit)g(p)s(oin)m(ts)f(of)0 1875 y(the)f(set)g(of)f(maxima)i
(attaining)e Fs(g)t Fu(\()p Fs(S)6 b Fu(\))31 b(in)i(\(2\)?)100
2046 y(W)-8 b(e)25 b(feel)h(that)f(a)g(p)s(ositiv)m(e)i(answ)m(er)g(to)
e(this)h(question)g(w)m(ould)h(pro)m(vide)f(a)f(further)h(natural)f
(justi\014cation)0 2162 y(for)31 b(studying)h Fs(g)t
Fu(\()p Fs(S)6 b Fu(\))30 b(in)i(place)f(of)g Fs(f)11
b Fu(\()p Fs(S)6 b Fu(\))31 b(when)h(the)f(former)h(is)f(more)h
(tractable.)43 b(Similarly)-8 b(,)33 b(it)e(w)m(ould)h(b)s(e)0
2279 y(in)m(teresting)i(to)e(get)h(conditions)h(on)e
Fs(S)38 b Fu(suc)m(h)c(that)f Fs(f)11 b Fu(\()p Fs(S)6
b Fu(\))32 b(is)h(not)f(m)m(uc)m(h)i(larger)f(than)f
Fs(g)t Fu(\()p Fs(S)6 b Fu(\).)100 2395 y(W)-8 b(e)33
b(are)f(also)h(curious)g(ab)s(out)f(the)h(exp)s(ected)i(v)-5
b(alues)33 b(of)g Fs(f)11 b Fu(\()p Fs(S)6 b Fu(\))31
b(and)i Fs(g)t Fu(\()p Fs(S)6 b Fu(\):)0 2566 y FA(Question)36
b(5.5.)k Fu(Giv)m(en)31 b Fs(n)g Fu(p)s(oin)m(ts)g(in)g
Fr(R)1528 2530 y Fq(d)1599 2566 y Fu(distributed)h(indep)s(enden)m(tly)
h(and)e(symmetrically)i(ab)s(out)d FA(0)p Fu(,)0 2682
y(what)k(is)g(the)g(exp)s(ected)h(deep)s(est)g(simplicial)g(depth)g(of)
e(the)h(resulting)g(con\014guration?)46 b(That)34 b(is,)h(what)0
2799 y(is)e(the)g(exp)s(ected)i(depth)e(of)f(the)h(simplicial)h(median)
g(of)e(the)h(p)s(oin)m(ts?)100 2970 y(W)-8 b(agner)31
b(and)g(W)-8 b(elzl)32 b([WW01])g(giv)m(e)g(an)f(expression)i(for)e
(the)g(exp)s(ected)i(depth)f(of)f FA(0)p Fu(,)h(but)f
FA(0)g Fu(will)h(not)0 3086 y(alw)m(a)m(ys)42 b(b)s(e)e(the)h(deep)s
(est)h(p)s(oin)m(t.)67 b(Indeed)41 b(if)f Fs(n)h Fu(=)g
Fs(d)27 b Fu(+)g(1)40 b(the)h(exp)s(ected)h(simplicial)g(depth)f(of)f
FA(0)g Fu(will)0 3202 y(b)s(e)164 3163 y Fo(1)p 145 3180
72 4 v 145 3237 a(2)180 3218 y Fi(d)262 3202 y Fu(while)d(the)e
(simplicial)i(median)f(alw)m(a)m(ys)h(has)f(depth)g(1.)51
b(F)-8 b(or)35 b(\014xed)h Fs(d)f Fu(the)h(exp)s(ected)h(depth)f(of)f
FA(0)0 3330 y Fu(is)126 3291 y Fo(1)p 108 3307 V 108
3365 a(2)143 3346 y Fi(d)189 3249 y Fk(\000)277 3286
y Fq(n)235 3364 y(d)p Fo(+1)361 3249 y Fk(\001)439 3330
y Fu(whic)m(h)f(has)f(the)f(same)h(asymptotic)h(b)s(eha)m(viour)f(as)f
(B\023)-49 b(ar\023)g(an)m(y's)34 b(sharp)e(upp)s(er)h(b)s(ound)g
(\(4\))e(for)0 3454 y Fs(g)t Fu(\()p Fs(S)6 b Fu(\).)41
b(Ho)m(w)m(ev)m(er,)32 b(when)e Fs(n)f Fu(is)h(not)f(m)m(uc)m(h)h
(larger)f(than)g(\()p Fs(d)15 b Fu(+)g(1\),)28 b(the)h(gap)g(b)s(et)m
(w)m(een)i(the)e(exp)s(ected)i(depth)0 3571 y(of)36 b
FA(0)h Fu(and)g(B\023)-49 b(ar\023)g(an)m(y's)37 b(upp)s(er)h(b)s(ound)
f(is)g(substan)m(tial)h(and)f(it)f(is)i(not)e(clear)h(to)g(us)g(where)h
(the)f(exp)s(ected)0 3687 y(depth)c(of)f(the)h(simplicial)i(median)e
(lies.)100 3803 y(B\023)-49 b(ar\023)g(an)m(y's)27 b(metho)s(d)h(of)e
(pro)m(ving)i(\(3\))e(com)m(bined)i(with)g(a)e(solution)i(to)e
(Question)i(5.1)e(migh)m(t)i(lend)f(some)0 3919 y(insigh)m(t)34
b(in)m(to)e(Question)i(5.5,)e(but)h(a)f(direct)i(approac)m(h)f(w)m
(ould)g(b)s(e)g(b)s(etter.)1421 4117 y(6.)48 b Ft(A)m(ckno)n
(wledgments)100 4291 y Fu(W)-8 b(e)33 b(w)m(ould)g(lik)m(e)h(to)e
(thank)h Ft(Imre)38 b(B)1477 4283 y(\023)1474 4291 y(ar)1598
4283 y(\023)1595 4291 y(any)33 b Fu(for)f(discussions)j(whic)m(h)f
(triggered)f(this)g(w)m(ork)h(and)f(the)0 4407 y(anon)m(ymous)h
(referees)g(for)e(suggestions)i(whic)m(h)g(impro)m(v)m(ed)h(the)e
(presen)m(tation)h(of)e(this)h(pap)s(er.)1660 4605 y
Ft(References)0 4763 y Fz([ABFK92])40 b(N.)31 b(Alon,)h(I.)e(B\023)-42
b(ar\023)g(an)n(y)-7 b(,)30 b(Z.)g(F)r(\177)-44 b(uredi,)32
b(and)e(D.)h(J.)f(Kleitman,)i Fm(Point)g(sele)l(ctions)h(and)g(we)l(ak)
h Fx(\017)p Fm(-nets)d(for)i(c)l(onvex)410 4862 y(hul)t(ls)p
Fz(,)c(Com)n(bin.)e(Probab.)f(Comput.)i Fc(1)g Fz(\(1992\),)e(no.)h(3,)
h(189{200.)0 4962 y([Alo04])153 b(G.)28 b(Aloupis,)g
Fm(Ge)l(ometric)j(me)l(asur)l(es)e(of)i(data)f(depth)p
Fz(,)f(submitted,)g(2004.)0 5062 y([Bak78])135 b(M.)28
b(J.)g(C.)f(Bak)n(er,)f Fm(Covering)32 b(with)e(triangles)g(III)p
Fz(,)e(James)f(Co)r(ok)g(Mathematical)g(Notes)g Fc(17)g
Fz(\(1978\),)g(11.)0 5161 y([B\023)-42 b(ar82])146 b(I.)31
b(B\023)-42 b(ar\023)g(an)n(y)-7 b(,)30 b Fm(A)i(gener)l(alization)i
(of)f(Car)l(ath)n(\023)-40 b(eo)l(dory's)36 b(the)l(or)l(em)p
Fz(,)31 b(Discrete)g(Math.)f Fc(40)g Fz(\(1982\),)h(no.)f(2-3,)g(141{)
410 5261 y(152.)p eop end
%%Page: 18 18
TeXDict begin 18 17 bop 0 75 a Fl(18)498 b(ANTOINE)25
b(DEZA,)g(SUI)f(HUANG,)h(T)-6 b(AMON)25 b(STEPHEN)h(AND)e(T)-6
b(AM)2823 56 y(\023)2813 75 y(AS)25 b(TERLAKY)0 274 y
Fz([BM05])145 b(I.)28 b(B\023)-42 b(ar\023)g(an)n(y)26
b(and)h(J.)h(Matou)l(\024)-37 b(sek,)25 b Fm(Quadr)l(atic)l(al)t(ly)32
b(many)e(c)l(olorful)h(simplic)l(es)p Fz(,)e(submitted,)g(2005.)0
373 y([BO97a])114 b(I.)26 b(B\023)-42 b(ar\023)g(an)n(y)24
b(and)i(S.)g(Onn,)g Fm(Car)l(ath)n(\023)-40 b(eo)l(dory's)31
b(the)l(or)l(em,)e(c)l(olourful)g(and)g(applic)l(able)p
Fz(,)g(In)n(tuitiv)n(e)d(geometry)e(\(Bu-)410 473 y(dap)r(est,)i
(1995\),)e(Boly)n(ai)f(So)r(c.)i(Math.)g(Stud.,)h(v)n(ol.)e(6,)h(J\023)
-42 b(anos)24 b(Boly)n(ai)f(Math.)i(So)r(c.,)g(Budap)r(est,)h(1997,)d
(pp.)i(11{)410 573 y(21.)0 672 y([BO97b])p 410 672 250
4 v 373 w(,)i Fm(Colourful)k(line)l(ar)e(pr)l(o)l(gr)l(amming)h(and)g
(its)f(r)l(elatives)p Fz(,)f(Math.)f(Op)r(er.)f(Res.)h
Fc(22)f Fz(\(1997\),)g(no.)g(3,)h(550{)410 772 y(567.)0
872 y([BF84])167 b(E.)24 b(Boros)e(and)i(Z.)g(F)r(\177)-44
b(uredi,)25 b Fm(The)i(numb)l(er)f(of)h(triangles)g(c)l(overing)h(the)e
(c)l(enter)g(of)i(an)e Fx(n)p Fm(-set)p Fz(,)e(Geom.)g(Dedicata)410
971 y Fc(17)k Fz(\(1984\),)e(no.)h(1,)h(69{77.)0 1071
y([CO01])155 b(A.)27 b(Y.)g(Cheng)g(and)f(M.)h(Ouy)n(ang,)e
Fm(On)j(algorithms)i(for)g(simplicial)h(depth)p Fz(,)d(Pro)r(ceedings)d
(of)h(the)h(13th)f(Cana-)410 1171 y(dian)i(Conference)f(on)g
(Computational)g(Geometry)-7 b(,)27 b(2001,)f(pp.)i(53{56.)0
1270 y([FR05])165 b(K.)26 b(F)-7 b(ukuda)26 b(and)g(V.)g(Rosta,)g
Fm(Data)i(depth)h(and)g(maximal)g(fe)l(asible)h(subsystems)p
Fz(,)c(Graph)f(Theory)g(and)h(Com-)410 1370 y(binatorial)h
(Optimization)h(\(D.)h(Avis,)e(A.)i(Hertz,)f(and)f(O.)h(Marcotte,)f
(eds.\),)h(Springer-V)-7 b(erlag,)26 b(New)i(Y)-7 b(ork,)410
1469 y(2005,)26 b(pp.)i(37{67.)0 1569 y([GSW92])84 b(J.)31
b(Gil,)h(W.)f(Steiger,)g(and)g(A.)g(Wigderson,)f Fm(Ge)l(ometric)k(me)l
(dians)p Fz(,)e(Discrete)f(Math.)f Fc(108)h Fz(\(1992\),)f(no.)g(1-3,)
410 1669 y(37{51.)0 1768 y([K\023)-42 b(ar55])140 b(F.)29
b(K\023)-42 b(arteszi,)26 b Fm(Extr)l(emalaufgab)l(en)32
b(\177)-43 b(ub)l(er)29 b(end)t(liche)j(Punktsysteme)p
Fz(,)c(Publ.)g(Math.)g(Debrecen)f Fc(4)h Fz(\(1955\),)e(16{)410
1868 y(27.)0 1968 y([Liu90])159 b(R.)28 b(Y.)g(Liu,)g
Fm(On)h(a)h(notion)g(of)h(data)g(depth)f(b)l(ase)l(d)h(on)f(r)l(andom)g
(simplic)l(es)p Fz(,)f(Ann.)f(Statist.)h Fc(18)e Fz(\(1990\),)f(no.)h
(1,)410 2067 y(405{414.)0 2167 y([Mun84])112 b(J.)20
b(R.)h(Munkres,)g Fm(Elements)i(of)h(algebr)l(aic)g(top)l(olo)l(gy)p
Fz(,)g(Addison-W)-7 b(esley)20 b(Publishing)f(Compan)n(y)-7
b(,)21 b(Menlo)f(P)n(ark,)410 2266 y(CA,)28 b(1984.)0
2366 y([ST05])174 b(T.)32 b(Stephen)g(and)g(H.)g(Thomas,)g
Fm(A)h(quadr)l(atic)h(lower)g(b)l(ound)g(for)g(c)l(olourful)g
(simplicial)i(depth)p Fz(,)e(submitted.)410 2466 y(arXiv:)p
Fb(math.CO/0512400)p Fz(,)21 b(2005.)0 2565 y([W)-7 b(ag03])118
b(U.)29 b(W)-7 b(agner,)27 b Fm(On)j(k-sets)f(and)i(applic)l(ations)p
Fz(,)g(Ph.D.)d(thesis,)g(ETH)g(Z)r(\177)-44 b(uric)n(h,)27
b(Departmen)n(t)h(of)g(Mathematics,)410 2665 y(2003.)0
2765 y([WW01])110 b(U.)30 b(W)-7 b(agner)29 b(and)g(E.)g(W)-7
b(elzl,)30 b Fm(A)h(c)l(ontinuous)g(analo)l(gue)h(of)h(the)e(upp)l(er)h
(b)l(ound)f(the)l(or)l(em)p Fz(,)g(Discrete)e(Comput.)410
2864 y(Geom.)f Fc(26)f Fz(\(2001\),)f(no.)i(2,)f(205{219.)0
2966 y([)28 2945 y(\024)23 2966 y(ZV92])167 b(R.)36 b(T.)654
2945 y(\024)649 2966 y(Ziv)-5 b(aljevi)n(\023)-39 b(c)34
b(and)i(S.)g(T.)g(V)-7 b(re)n(\023)-39 b(cica,)35 b Fm(The)k(c)l(olor)l
(e)l(d)f(Tverb)l(er)l(g's)g(pr)l(oblem)g(and)g(c)l(omplexes)g(of)g
(inje)l(ctive)410 3066 y(functions)p Fz(,)28 b(J.)g(Com)n(bin.)f
(Theory)g(Ser.)g(A)h Fc(61)f Fz(\(1992\),)f(no.)i(2,)f(309{318.)100
3253 y Fy(Ad)n(v)-7 b(anced)40 b(Optimiza)-6 b(tion)42
b(Labora)-6 b(tor)g(y,)44 b(Dep)-6 b(ar)g(tment)43 b(of)f(Computing)g
(and)f(Softw)-7 b(are,)43 b(F)-10 b(a)n(cul)k(ty)0 3352
y(of)27 b(Engineering,)h(1280)e(Main)h(St.)f(West,)i(McMaster)f
(University,)h(Hamil)-6 b(ton,)26 b(Ont)-6 b(ario,)28
b(Canad)n(a)f(L8S)0 3452 y(4K1.)100 3552 y Fm(E-mail)j(addr)l(ess)7
b Fz(:)38 b Fa(f)p Fb(deza,huangs3)p Fa(g)p Fb(@mc)o(ma)o(st)o(er.)o
(ca)o(,)g(tamon@optlab.mc)o(mas)o(te)o(r.)o(ca,)f(terlaky@mcmaster)o
(.c)o(a)p eop end
%%Trailer

userdict /end-hook known{end-hook}if
%%EOF