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cleartomark
%%EndFont
%%BeginFont: CMSY5
%!PS-AdobeFont-1.1: CMSY5 1.0
%%CreationDate: 1991 Aug 15 07:21:16
% 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 (CMSY5) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY5 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 26 /propersubset put
dup 48 /prime put
readonly def
/FontBBox{21 -944 1448 791}readonly def
/UniqueID 5000815 def
currentdict end
currentfile eexec
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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 80 /summationtext put
dup 88 /summationdisplay put
readonly def
/FontBBox{-24 -2960 1454 772}readonly def
/UniqueID 5000774 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMBXSL10
%!PS-AdobeFont-1.1: CMBXSL10 1.0
%%CreationDate: 1991 Aug 20 16:36:44
% 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 (CMBXSL10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Bold) readonly def
/ItalicAngle -9.46 def
/isFixedPitch false def
end readonly def
/FontName /CMBXSL10 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 40 /parenleft put
dup 41 /parenright put
dup 44 /comma put
dup 48 /zero put
dup 50 /two put
dup 52 /four put
dup 67 /C put
dup 69 /E put
dup 71 /G put
dup 83 /S put
dup 87 /W put
dup 97 /a put
dup 101 /e put
dup 104 /h put
dup 105 /i put
dup 108 /l put
dup 110 /n put
dup 112 /p put
dup 116 /t put
dup 118 /v put
readonly def
/FontBBox{-75 -250 1278 750}readonly def
/UniqueID 5000770 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMSY7
%!PS-AdobeFont-1.1: CMSY7 1.0
%%CreationDate: 1991 Aug 15 07:21:52
% 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 (CMSY7) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.035 def
/isFixedPitch false def
end readonly def
/FontName /CMSY7 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 26 /propersubset put
dup 48 /prime put
dup 59 /emptyset put
dup 91 /union put
dup 102 /braceleft put
dup 103 /braceright put
dup 106 /bar put
dup 110 /backslash put
readonly def
/FontBBox{-15 -951 1252 782}readonly def
/UniqueID 5000817 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMMI5
%!PS-AdobeFont-1.1: CMMI5 1.100
%%CreationDate: 1996 Aug 02 08:21:10
% 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 (CMMI5) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI5 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 73 /I put
dup 86 /V put
dup 87 /W put
readonly def
/FontBBox{37 -250 1349 750}readonly def
/UniqueID 5087380 def
currentdict end
currentfile eexec
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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 59 /comma put
dup 61 /slash put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 73 /I put
dup 86 /V put
dup 87 /W 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 112 /p put
dup 118 /v put
readonly def
/FontBBox{0 -250 1171 750}readonly def
/UniqueID 5087382 def
currentdict end
currentfile eexec
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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 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 55 /seven put
dup 57 /nine put
dup 61 /equal put
readonly def
/FontBBox{-27 -250 1122 750}readonly def
/UniqueID 5000790 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%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 3 /asteriskmath put
dup 18 /reflexsubset put
dup 20 /lessequal put
dup 21 /greaterequal put
dup 24 /similar put
dup 26 /propersubset put
dup 50 /element 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
/UniqueID 5000820 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMTT8
%!PS-AdobeFont-1.1: CMTT8 1.0
%%CreationDate: 1991 Aug 20 16:46:05
% 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 (CMTT8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch true def
end readonly def
/FontName /CMTT8 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 46 /period put
dup 64 /at 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 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 122 /z put
readonly def
/FontBBox{-5 -232 545 699}readonly def
/UniqueID 5000830 def
currentdict end
currentfile eexec
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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 3 /asteriskmath put
dup 110 /backslash put
readonly def
/FontBBox{-30 -955 1185 779}readonly def
/UniqueID 5000818 def
currentdict end
currentfile eexec
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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 25 /pi put
dup 58 /period put
dup 59 /comma put
dup 60 /less put
dup 61 /slash put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 79 /O put
dup 83 /S put
dup 84 /T put
dup 86 /V put
dup 87 /W put
dup 97 /a put
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dup 107 /k put
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dup 110 /n put
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readonly def
/FontBBox{-32 -250 1048 750}readonly def
/UniqueID 5087385 def
currentdict end
currentfile eexec
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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 40 /parenleft put
dup 41 /parenright put
dup 44 /comma put
dup 45 /hyphen put
dup 46 /period put
dup 49 /one put
dup 53 /five put
dup 58 /colon put
dup 67 /C put
dup 68 /D put
dup 70 /F put
dup 72 /H put
dup 73 /I put
dup 76 /L put
dup 80 /P 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 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
readonly def
/FontBBox{-163 -250 1146 969}readonly def
/UniqueID 5000828 def
currentdict end
currentfile eexec
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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 2 /Theta put
dup 10 /Omega put
dup 11 /ff put
dup 12 /fi put
dup 13 /fl put
dup 14 /ffi put
dup 34 /quotedblright 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 61 /equal 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 76 /L put
dup 77 /M put
dup 78 /N put
dup 79 /O put
dup 80 /P put
dup 83 /S put
dup 84 /T put
dup 85 /U put
dup 87 /W 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 123 /endash put
readonly def
/FontBBox{-251 -250 1009 969}readonly def
/UniqueID 5000793 def
currentdict end
currentfile eexec
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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 40 /parenleft put
dup 41 /parenright 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 67 /C put
dup 69 /E put
dup 71 /G put
dup 73 /I put
dup 76 /L put
dup 77 /M put
dup 82 /R put
dup 83 /S put
dup 84 /T 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 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 121 /y put
readonly def
/FontBBox{-301 -250 1164 946}readonly def
/UniqueID 5000768 def
currentdict end
currentfile eexec
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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 12 /fi put
dup 44 /comma put
dup 45 /hyphen put
dup 46 /period 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 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
readonly def
/FontBBox{-39 -250 1036 750}readonly def
/UniqueID 5000792 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMBX9
%!PS-AdobeFont-1.1: CMBX9 1.0
%%CreationDate: 1991 Aug 20 16:36:25
% 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 (CMBX9) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Bold) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMBX9 def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] readonly def
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dup 65 /A put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 114 /r put
dup 115 /s put
dup 116 /t put
readonly def
/FontBBox{-58 -250 1195 750}readonly def
/UniqueID 5000767 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMTI8
%!PS-AdobeFont-1.1: CMTI8 1.0
%%CreationDate: 1991 Aug 18 21:07:42
% 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 (CMTI8) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMTI8 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 40 /parenleft put
dup 41 /parenright put
dup 44 /comma put
dup 45 /hyphen 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 54 /six put
dup 55 /seven put
dup 56 /eight put
dup 58 /colon 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 73 /I put
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dup 75 /K put
dup 76 /L put
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dup 80 /P put
dup 82 /R put
dup 83 /S put
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dup 104 /h put
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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 126 /tilde put
readonly def
/FontBBox{-35 -250 1190 750}readonly def
/UniqueID 5000826 def
currentdict end
currentfile eexec
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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 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 61 /equal put
dup 97 /a put
dup 98 /b put
dup 99 /c put
dup 100 /d put
readonly def
/FontBBox{-20 -250 1193 750}readonly def
/UniqueID 5000789 def
currentdict end
currentfile eexec
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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 25 /pi put
dup 59 /comma put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 97 /a put
dup 105 /i put
dup 108 /l put
dup 109 /m put
dup 118 /v put
readonly def
/FontBBox{-24 -250 1110 750}readonly def
/UniqueID 5087383 def
currentdict end
currentfile eexec
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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 13 /fl put
dup 16 /dotlessi put
dup 18 /grave put
dup 19 /acute put
dup 38 /ampersand put
dup 40 /parenleft put
dup 41 /parenright put
dup 44 /comma put
dup 45 /hyphen 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 54 /six put
dup 55 /seven put
dup 56 /eight put
dup 57 /nine put
dup 58 /colon put
dup 61 /equal 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
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dup 85 /U put
dup 86 /V 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 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 123 /endash put
dup 126 /tilde put
readonly def
/FontBBox{-36 -250 1070 750}readonly def
/UniqueID 5000791 def
currentdict end
currentfile eexec
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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 44 /comma put
dup 49 /one put
dup 65 /A put
dup 66 /B put
dup 68 /D put
dup 70 /F put
dup 79 /O put
dup 83 /S put
dup 97 /a put
dup 99 /c put
dup 100 /d put
dup 101 /e 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 118 /v put
dup 119 /w put
dup 122 /z put
readonly def
/FontBBox{-34 -251 988 750}readonly def
/UniqueID 5000794 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont
%%BeginFont: CMR17
%!PS-AdobeFont-1.1: CMR17 1.0
%%CreationDate: 1991 Aug 20 16:38:24
% 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 (CMR17) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR17 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 45 /hyphen put
dup 67 /C put
dup 78 /N put
dup 79 /O put
dup 80 /P put
dup 83 /S put
dup 84 /T put
dup 97 /a put
dup 98 /b 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 108 /l put
dup 109 /m put
dup 110 /n put
dup 111 /o put
dup 114 /r put
dup 115 /s put
dup 116 /t put
dup 117 /u put
readonly def
/FontBBox{-33 -250 945 749}readonly def
/UniqueID 5000795 def
currentdict end
currentfile eexec
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Fh(I)2473 5000 y Fn(and)j(for)h(every)g Fm(v)g Fj(2)e
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Fn(PT)3014 5153 y Fh(W)9 b Ff(nf)p Fh(v)r Ff(g)3227 5138
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cleartomark
%%EndResource
/F4_0 /OSBDAF+CMMI10 1 1
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pdfMakeFont
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%!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 /ASDWAB+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 99 /c put
dup 114 /r put
readonly def
/FontBBox{0 -250 1171 750}readonly def
/UniqueID 5087382 def
currentdict end
currentfile eexec
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cleartomark
%%EndResource
/F7_0 /ASDWAB+CMMI7 1 1
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pdfMakeFont
%%BeginResource: font EECPQT+CMR5
%!PS-AdobeFont-1.1: CMR5 1.00B
%%CreationDate: 1992 Feb 19 19:55:02
% 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 (CMR5) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /EECPQT+CMR5 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 51 /three put
readonly def
/FontBBox{-341 -250 1304 965}readonly def
/UniqueID 5000788 def
currentdict end
currentfile eexec
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cleartomark
%%EndResource
/F10_0 /EECPQT+CMR5 1 1
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@endspecial 2260 1018 a Fw(Fig.)h(1.)f(A)g(double)g(c)n(hain:)g
Fv(l)c Fw(=)g(5)k(and)g Fv(m)c Fw(=)f(4.)1993 1201 y
Fp(2.)47 b(The)25 b(double)f(circle)h(and)g(its)f(relativ)m(es)2076
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Fo(,)28 b(3)g Fj(\024)g Fm(i)g Fj(\024)g Fm(v)s Fo(,)h(and)f(let)g
Fm(A)h Fo(b)r(e)f(a)1993 1446 y(p)r(oin)n(t)h(set)f(in)i(almost)e(con)n
(v)n(ex)f(p)r(osition)i(with)g(parame-)1993 1545 y(ters)j(\()p
Fm(v)s(;)14 b(i)p Fo(\).)33 b(Let)g Fm(p)f Fo(b)r(e)h(a)g(sp)r
(eci\014c)g(in)n(terior)e(p)r(oin)n(t)i(of)g Fm(A)1993
1645 y Fo(and)19 b(let)g Fm(q)s(r)k Fo(b)r(e)c(the)h(con)n(v)n(ex)e(h)n
(ull)i(edge)e(whic)n(h)i(has)e Fm(p)i Fo(next)1993 1745
y(to)28 b(it.)i(Let)f Fm(B)k Fo(and)c Fm(C)35 b Fo(b)r(e)29
b(the)g(p)r(oin)n(t)g(sets)g(obtained)g(re-)1993 1844
y(sp)r(ectiv)n(ely)g(b)n(y)g(deleting)g Fm(p)g Fo(from)h
Fm(A)f Fo(and)h(b)n(y)f(mo)n(ving)f Fm(p)1993 1944 y
Fo(to)c(con)n(v)n(ex)g(p)r(osition)g(across)f(the)i(con)n(v)n(ex)f(h)n
(ull)h(edge)f Fm(q)s(r)r Fo(:)1993 2681 y @beginspecial
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99.0997 441.842 100.862 440.085 103.037 440.085 c
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h
f*
Q
q
q
0.4 w
0.75 g
104.587 444.01 m
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102.18 445.555 101.486 444.864 101.486 444.01 c
101.486 443.157 102.18 442.465 103.037 442.465 c
103.893 442.465 104.587 443.157 104.587 444.01 c
h
f*
104.587 444.01 m
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101.486 443.157 102.18 442.465 103.037 442.465 c
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h
S
Q
Q
q
q
q
0.4 w
1 g
110.166 468.171 m
110.166 470.339 108.403 472.096 106.229 472.096 c
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h
f*
Q
q
q
0.4 w
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107.779 468.172 m
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h
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107.779 468.172 m
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107.085 466.626 107.779 467.318 107.779 468.172 c
h
S
Q
Q
q
q
q
0.4 w
1 g
103.709 487.758 m
103.709 489.926 101.946 491.683 99.7715 491.683 c
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95.8344 485.591 97.5971 483.834 99.7715 483.834 c
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h
f*
Q
q
q
0.4 w
0.75 g
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98.2221 486.905 98.9161 486.213 99.7722 486.213 c
100.628 486.213 101.322 486.905 101.322 487.759 c
h
f*
101.322 487.759 m
101.322 488.612 100.628 489.304 99.7722 489.304 c
98.9161 489.304 98.2221 488.612 98.2221 487.759 c
98.2221 486.905 98.9161 486.213 99.7722 486.213 c
100.628 486.213 101.322 486.905 101.322 487.759 c
h
S
Q
Q
q
[1 0 0 1 109.781 466.88] cm
0 g
0 G
[1 0 0 1 0 -788.568] cm
[1 0 0 1 0 0] Tm
0 0 Td
0 788.568 Td
/F4_0 7.97 Tf
(r) 3.81763 Tj
Q
q
[1 0 0 1 106.659 440.081] cm
[1 0 0 1 0 1.55] cm
0 g
0 G
[1 0 0 1 0 -788.569] cm
[1 0 0 1 0 0] Tm
0 0 Td
0 788.569 Td
/F4_0 7.97 Tf
(q) 3.77778 Tj
Q
q
[1 0 0 1 81.2878 419.51] cm
0 g
0 G
[1 0 0 1 0 -786.554] cm
[1 0 0 1 0 0] Tm
0 0 Td
0 786.554 Td
/F4_0 7.97 Tf
(B) 6.38397 Tj
Q
Q
Q
Q
Q
Q
Q
Q
Q
Q
Q
Q
Q
Q
Q
Q
Q
Q
Q
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Q
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h
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h
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98.2221 486.905 98.9161 486.213 99.7722 486.213 c
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0 G
[1 0 0 1 0 -788.569] cm
[1 0 0 1 0 0] Tm
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0 788.569 Td
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Q
q
[1 0 0 1 109.781 466.88] cm
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(r) 3.81763 Tj
Q
q
[1 0 0 1 106.659 440.081] cm
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(q) 3.77778 Tj
Q
q
[1 0 0 1 81.2878 419.51] cm
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[1 0 0 1 0 -786.554] cm
[1 0 0 1 0 0] Tm
0 0 Td
0 786.554 Td
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(C) 6.03329 Tj
Q
Q
Q
Q
Q
Q
Q
Q
Q
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Q
Q
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@endspecial 2004 2805 a Fw(Fig.)g(2.)h(The)f(p)r(oin)n(t)h(sets)f
Fv(A)p Fw(,)f Fv(B)k Fw(and)d Fv(C)5 b Fw(.)23 b(Here)g
Fv(v)g Fw(=)c(9)24 b(and)g Fv(i)c Fw(=)f(4.)1993 2964
y Fp(Lemma)24 b(2)49 b Fn(L)l(et)28 b Fm(W)41 b Fn(b)l(e)29
b(a)g(set)f(of)i(interior)g(p)l(oints)f(of)h Fm(A)1993
3064 y Fn(not)20 b(c)l(ontaining)i Fm(p)f Fn(\(so)h(that)f
Fm(W)33 b Fn(is)22 b(also)g(a)g(set)f(of)h(interior)1993
3163 y(p)l(oints)j(of)h Fm(B)j Fn(and)c Fm(C)6 b Fn(\).)26
b(Then:)2063 3263 y(\(i\))42 b Fj(j)p Fn(PT)2348 3275
y Fh(W)2424 3263 y Fo(\()p Fm(A)p Fo(\))p Fj(j)24 b Fo(=)e
Fj(j)p Fn(PT)2834 3275 y Fh(W)2910 3263 y Fo(\()p Fm(C)6
b Fo(\))p Fj(j)19 b(\000)f(j)p Fn(PT)3314 3275 y Fh(W)3390
3263 y Fo(\()p Fm(B)t Fo(\))p Fj(j)p Fn(.)2037 3363 y(\(ii\))43
b Fj(j)p Fn(PT)2348 3378 y Fh(W)9 b Ff([f)p Fh(p)p Ff(g)2571
3363 y Fo(\()p Fm(A)p Fo(\))p Fj(j)24 b Fo(=)e(2)14 b
Fj(j)p Fn(PT)3037 3375 y Fh(W)3112 3363 y Fo(\()p Fm(C)6
b Fo(\))p Fj(j)19 b(\000)g(j)p Fn(PT)3516 3375 y Fh(W)3592
3363 y Fo(\()p Fm(B)t Fo(\))p Fj(j)p Fn(.)1993 3492 y
Fp(Corollary)24 b(3)119 b Fn(\(i\))43 b Fm(A)25 b Fn(satis\014es)g
(Conje)l(ctur)l(e)g(1.)2037 3592 y(\(ii\))43 b(The)28
b(numb)l(ers)f Fj(j)p Fn(PT)2842 3604 y Fh(W)2918 3592
y Fo(\()p Fm(A)p Fo(\))p Fj(j)h Fn(dep)l(end)g(only)f(on)h
Fm(v)s Fn(,)f Fm(i)2198 3692 y Fn(and)f Fm(k)g Fo(:=)d
Fj(j)p Fm(W)12 b Fj(j)p Fn(.)2076 3821 y Fo(W)-7 b(e)35
b(omit)g(the)g(pro)r(ofs)f(of)h(these)g(and)g(other)f(results)1993
3921 y(due)20 b(to)g(the)g(limited)h(space)e(a)n(v)-5
b(ailable)19 b(for)h(this)g(abstract.)2076 4021 y(Let)28
b Fm(n)p Fo(\()p Fm(v)s(;)14 b(i;)g(k)s Fo(\))28 b(denote)g(the)h(n)n
(um)n(b)r(ers)f(referred)f(to)h(in)1993 4120 y(part)15
b(2)h(of)g(the)h(corollary)-7 b(.)14 b(Since)i Fm(n)p
Fo(\()p Fm(v)s(;)e(i;)g Fo(0\))23 b(=)f(4)3442 4090 y
Fh(v)3481 4120 y Fo(3)3523 4090 y Fh(i)3567 4120 y Fo(\(mo)r(d-)1993
4220 y(ulo)i(a)h(p)r(olynomial)f(factor\))g(and)h(since)1993
4378 y Fm(n)p Fo(\()p Fm(v)s(;)14 b(i;)g(k)s Fo(\))22
b(=)h(2\()p Fm(v)16 b Fo(+)d(1)p Fm(;)h(i)f Fj(\000)g
Fo(1)p Fm(;)h(k)f Fj(\000)g Fo(1\))g Fj(\000)g Fm(n)p
Fo(\()p Fm(v)s(;)h(i)f Fj(\000)g Fo(1)p Fm(;)h(k)f Fj(\000)g
Fo(1\))p Fm(;)1993 4535 y Fo(w)n(e)28 b(conclude)h(that)h
Fm(n)p Fo(\()p Fm(v)s(;)14 b(i;)g(k)s Fo(\))30 b Fj(\030)g
Fo(4)3114 4505 y Fh(v)3153 4535 y Fo(3)3195 4505 y Fh(i)p
Ff(\000)p Fh(k)3310 4535 y Fo(7)3352 4505 y Fh(k)3393
4535 y Fm(;)f Fo(mo)r(dulo)g(a)1993 4635 y(p)r(olynomial)16
b(factor.)g(Adding)h(the)g(n)n(um)n(b)r(ers)f(o)n(v)n(er)f(all)h(the)
1993 4735 y(p)r(ossible)24 b(subsets)h(of)f(in)n(terior)g(p)r(oin)n(ts)
h(giv)n(es)2463 4864 y Fh(i)2415 4889 y Fd(X)2415 5068
y Fh(k)q Fi(=0)2549 4851 y Fd(\022)2619 4912 y Fm(i)2610
5025 y(k)2656 4851 y Fd(\023)2717 4968 y Fo(4)2759 4933
y Fh(v)2798 4968 y Fo(3)2840 4933 y Fh(i)p Ff(\000)p
Fh(k)2956 4968 y Fo(7)2998 4933 y Fh(k)3061 4968 y Fo(=)e(4)3191
4933 y Fh(v)3230 4968 y Fo(10)3314 4933 y Fh(i)3341 4968
y Fm(:)1993 5205 y Fo(Hence,)39 b(a)f(double)h(circle)f(\(the)i(case)e
Fm(i)46 b Fo(=)g Fm(v)j Fo(=)d Fm(n=)p Fo(2\))1993 5313
y(has)2131 5245 y Fj(p)p 2200 5245 V 68 x Fo(28)2283
5259 y Fh(n)2347 5313 y Fo(p)r(oin)n(ted)18 b(pseudo-triangulations)e
(and)3588 5245 y Fj(p)p 3658 5245 V 3658 5313 a Fo(40)3741
5259 y Fh(n)1993 5413 y Fo(pseudo-triangulations)30 b(in)k(total,)f(mo)
r(dulo)g(a)g(p)r(olyno-)1993 5513 y(mial)24 b(factor.)p
eop end
%%Page: 3 3
TeXDict begin 3 2 bop 0 83 a Fp(Marc)m(h)26 b(25-26,)d(2004)2424
b(Seville)23 b(\(Spain\))0 531 y(3.)47 b(The)25 b(single)e(c)m(hain)83
652 y Fo(As)e(a)g(step)g(to)n(w)n(ards)e(the)j(study)f(of)g(the)h
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Fo(has)f Fm(l)23 b Fo(+)d Fm(m)h Fo(+)1993 3719 y(4)36
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exch 1 array astore composefont pop
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pdfMakeFont16
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% graphics state operators
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/j { setlinejoin } def
/J { setlinecap } def
/M { setmiterlimit } def
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% color operators
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findcmykcustomcolor exch setcustomcolor
/pdfLastFill true def /pdfLastStroke false def } def
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findcmykcustomcolor exch setcustomcolor
/pdfLastStroke true def /pdfLastFill false def } def
% path segment operators
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/l { lineto } def
/c { curveto } def
/re { 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto
neg 0 rlineto closepath } def
/h { closepath } def
% path painting operators
/S { sCol stroke } def
/Sf { fCol stroke } def
/f { fCol fill } def
/f* { fCol eofill } def
% clipping operators
/W { clip newpath } def
/W* { eoclip newpath } def
% text state operators
/Tc { /pdfCharSpacing exch def } def
/Tf { dup /pdfFontSize exch def
dup pdfHorizScaling mul exch matrix scale
pdfTextMat matrix concatmatrix dup 4 0 put dup 5 0 put
exch findfont exch makefont setfont } def
/Tr { /pdfTextRender exch def } def
/Ts { /pdfTextRise exch def } def
/Tw { /pdfWordSpacing exch def } def
/Tz { /pdfHorizScaling exch def } def
% text positioning operators
/Td { pdfTextMat transform moveto } def
/Tm { /pdfTextMat exch def } def
% text string operators
/awcp { % awidthcharpath
exch {
1 string dup 0 3 index put 2 index charpath
3 index 3 index rmoveto
4 index eq { 5 index 5 index rmoveto } if
} forall
6 {pop} repeat
} def
/Tj { fCol
0 pdfTextRise pdfTextMat dtransform rmoveto
1 index stringwidth pdfTextMat idtransform pop
sub 1 index length dup 0 ne { div } { pop pop 0 } ifelse
pdfWordSpacing pdfHorizScaling mul 0 pdfTextMat dtransform 32
4 3 roll pdfCharSpacing pdfHorizScaling mul add 0
pdfTextMat dtransform
6 5 roll
currentpoint 8 2 roll
pdfTextRender 1 and 0 eq {
6 copy awidthshow
} if
pdfTextRender 3 and dup 1 eq exch 2 eq or {
8 6 roll moveto
currentfont /FontType get 3 eq { fCol } { sCol } ifelse
false awcp currentpoint stroke moveto
} {
8 {pop} repeat
} ifelse
0 pdfTextRise neg pdfTextMat dtransform rmoveto } def
/Tj16 { pdfTextRender 1 and 0 eq { fCol } { sCol } ifelse
0 pdfTextRise pdfTextMat dtransform rmoveto
2 index stringwidth pdfTextMat idtransform pop
sub exch div
pdfWordSpacing pdfHorizScaling mul 0 pdfTextMat dtransform 32
4 3 roll pdfCharSpacing pdfHorizScaling mul add 0
pdfTextMat dtransform
6 5 roll awidthshow
0 pdfTextRise neg pdfTextMat dtransform rmoveto } def
/Tj16V { pdfTextRender 1 and 0 eq { fCol } { sCol } ifelse
0 pdfTextRise pdfTextMat dtransform rmoveto
2 index stringwidth pdfTextMat idtransform exch pop
sub exch div
0 pdfWordSpacing pdfTextMat dtransform 32
4 3 roll pdfCharSpacing add 0 exch
pdfTextMat dtransform
6 5 roll awidthshow
0 pdfTextRise neg pdfTextMat dtransform rmoveto } def
/TJm { pdfFontSize 0.001 mul mul neg 0
pdfTextMat dtransform rmoveto } def
/TJmV { pdfFontSize 0.001 mul mul neg 0 exch
pdfTextMat dtransform rmoveto } def
% Level 1 image operators
/pdfIm1 {
/pdfImBuf1 4 index string def
{ currentfile pdfImBuf1 readhexstring pop } image
} def
/pdfIm1Sep {
/pdfImBuf1 4 index string def
/pdfImBuf2 4 index string def
/pdfImBuf3 4 index string def
/pdfImBuf4 4 index string def
{ currentfile pdfImBuf1 readhexstring pop }
{ currentfile pdfImBuf2 readhexstring pop }
{ currentfile pdfImBuf3 readhexstring pop }
{ currentfile pdfImBuf4 readhexstring pop }
true 4 colorimage
} def
/pdfImM1 {
/pdfImBuf1 4 index 7 add 8 idiv string def
{ currentfile pdfImBuf1 readhexstring pop } imagemask
} def
% Level 2 image operators
/pdfImBuf 100 string def
/pdfIm {
image
{ currentfile pdfImBuf readline
not { pop exit } if
(%-EOD-) eq { exit } if } loop
} def
/pdfImSep {
findcmykcustomcolor exch
dup /Width get /pdfImBuf1 exch string def
begin Width Height BitsPerComponent ImageMatrix DataSource end
/pdfImData exch def
{ pdfImData pdfImBuf1 readstring pop
0 1 2 index length 1 sub {
1 index exch 2 copy get 255 exch sub put
} for }
6 5 roll customcolorimage
{ currentfile pdfImBuf readline
not { pop exit } if
(%-EOD-) eq { exit } if } loop
} def
/pdfImM {
fCol imagemask
{ currentfile pdfImBuf readline
not { pop exit } if
(%-EOD-) eq { exit } if } loop
} def
end
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xpdf begin
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%121.935 498.534 m
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%
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%
%
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%
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pdfStartPage
[] 0 d
0 i
0 j
0 J
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0 G
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q
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S
Q
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S
Q
q
0.4 w
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S
Q
q
0.4 w
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S
Q
q
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S
Q
q
0.4 w
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S
Q
q
0.4 w
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S
Q
q
0.4 w
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S
Q
q
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S
Q
q
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S
Q
q
q
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h
f*
52.565 499.235 m
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51.871 497.69 52.565 498.382 52.565 499.235 c
h
S
Q
q
q
0.4 w
0.75 g
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h
f*
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h
S
Q
q
q
0.4 w
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h
f*
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h
S
Q
q
q
0.4 w
0.75 g
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h
f*
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h
S
Q
q
q
0.4 w
0.75 g
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85.7588 486.903 85.0648 486.211 85.0648 485.358 c
85.0648 484.504 85.7588 483.812 86.6149 483.812 c
87.471 483.812 88.165 484.504 88.165 485.358 c
h
f*
88.165 485.358 m
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85.0648 484.504 85.7588 483.812 86.6149 483.812 c
87.471 483.812 88.165 484.504 88.165 485.358 c
h
S
Q
q
q
0.4 w
0.75 g
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98.8818 488.71 98.1878 488.018 98.1878 487.165 c
98.1878 486.312 98.8818 485.62 99.7379 485.62 c
100.594 485.62 101.288 486.312 101.288 487.165 c
h
f*
101.288 487.165 m
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98.1878 486.312 98.8818 485.62 99.7379 485.62 c
100.594 485.62 101.288 486.312 101.288 487.165 c
h
S
Q
q
q
0.4 w
0.75 g
113.482 489.778 m
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110.382 488.925 111.076 488.233 111.932 488.233 c
112.788 488.233 113.482 488.925 113.482 489.778 c
h
f*
113.482 489.778 m
113.482 490.631 112.788 491.323 111.932 491.323 c
111.076 491.323 110.382 490.631 110.382 489.778 c
110.382 488.925 111.076 488.233 111.932 488.233 c
112.788 488.233 113.482 488.925 113.482 489.778 c
h
S
Q
q
q
0.4 w
0.75 g
61.659 453.197 m
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h
f*
61.659 453.197 m
61.659 454.051 60.965 454.742 60.1089 454.742 c
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58.5588 452.344 59.2528 451.652 60.1089 451.652 c
60.965 451.652 61.659 452.344 61.659 453.197 c
h
S
Q
q
q
0.4 w
0.75 g
79.659 455.955 m
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78.965 454.41 79.659 455.102 79.659 455.955 c
h
f*
79.659 455.955 m
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78.965 454.41 79.659 455.102 79.659 455.955 c
h
S
Q
q
q
0.4 w
0.75 g
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114.529 451.362 115.223 452.053 115.223 452.907 c
h
f*
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112.123 452.053 112.817 451.362 113.673 451.362 c
114.529 451.362 115.223 452.053 115.223 452.907 c
h
S
Q
q
q
0.4 w
0.75 g
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127.393 444.103 128.087 444.795 128.087 445.648 c
h
f*
128.087 445.648 m
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124.987 444.795 125.681 444.103 126.537 444.103 c
127.393 444.103 128.087 444.795 128.087 445.648 c
h
S
Q
q
q
0.4 w
0.75 g
100.852 455.81 m
100.852 456.663 100.158 457.355 99.3019 457.355 c
98.4458 457.355 97.7518 456.663 97.7518 455.81 c
97.7518 454.957 98.4458 454.265 99.3019 454.265 c
100.158 454.265 100.852 454.957 100.852 455.81 c
h
f*
100.852 455.81 m
100.852 456.663 100.158 457.355 99.3019 457.355 c
98.4458 457.355 97.7518 456.663 97.7518 455.81 c
97.7518 454.957 98.4458 454.265 99.3019 454.265 c
100.158 454.265 100.852 454.957 100.852 455.81 c
h
S
Q
q
q
0.4 w
0.75 g
123.485 498.534 m
123.485 499.387 122.791 500.079 121.935 500.079 c
121.079 500.079 120.385 499.387 120.385 498.534 c
120.385 497.681 121.079 496.989 121.935 496.989 c
122.791 496.989 123.485 497.681 123.485 498.534 c
h
f*
123.485 498.534 m
123.485 499.387 122.791 500.079 121.935 500.079 c
121.079 500.079 120.385 499.387 120.385 498.534 c
120.385 497.681 121.079 496.989 121.935 496.989 c
122.791 496.989 123.485 497.681 123.485 498.534 c
h
S
Q
Q
Q
Q
Q
Q
Q
Q
Q
Q
Q
Q
Q
Q
Q
showpage
%%PageTrailer
pdfEndPage
%%Trailer
end
%%DocumentSuppliedResources:
%%EOF
%%EndDocument
@endspecial 355 1498 a @beginspecial 80 @llx 438 @lly
210 @urx 506 @ury 1300 @rwi @setspecial
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%%BeginProlog
%%BeginResource: procset xpdf 2.01 0
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3 1 roll 2 array astore
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pop 3 dict begin
/PageSize exch def
/ImagingBBox null def
/Policies 1 dict dup begin /PageSize 3 def end def
{ /Duplex true def } if
currentdict end setpagedevice
} {
pop pop
} ifelse
} def
/pdfStartPage {
pdfDictSize dict begin
/pdfFill [0] def
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/pdfLastFill false def
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/pdfTextRender 0 def
/pdfTextRise 0 def
/pdfWordSpacing 0 def
/pdfHorizScaling 1 def
} def
/pdfEndPage { end } def
% separation convention operators
/findcmykcustomcolor where {
pop
}{
/findcmykcustomcolor { 5 array astore } def
} ifelse
/setcustomcolor where {
pop
}{
/setcustomcolor {
exch
[ exch /Separation exch dup 4 get exch /DeviceCMYK exch
0 4 getinterval cvx
[ exch /dup load exch { mul exch dup } /forall load
/pop load dup ] cvx
] setcolorspace setcolor
} def
} ifelse
/customcolorimage where {
pop
}{
/customcolorimage {
gsave
[ exch /Separation exch dup 4 get exch /DeviceCMYK exch
0 4 getinterval cvx
[ exch /dup load exch { mul exch dup } /forall load
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] setcolorspace
10 dict begin
/ImageType 1 def
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grestore
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% PDF color state
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dup 3 eq {
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4 eq {
setcmykcolor
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findcmykcustomcolor exch setcustomcolor
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/pdfLastStroke true def /pdfLastFill false def
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} def
/fCol {
pdfLastFill not {
pdfFill aload length
dup 1 eq {
pop setgray
}{
dup 3 eq {
pop setrgbcolor
}{
4 eq {
setcmykcolor
}{
findcmykcustomcolor exch setcustomcolor
} ifelse
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/pdfLastFill true def /pdfLastStroke false def
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% build a font
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4 2 roll matrix scale makefont
dup length dict begin
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currentdict
end
definefont pop
} def
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dup length dict begin
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end
definefont pop
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1 index /CIDFont resourcestatus {
pop pop 1 index /CIDFont findresource /CIDFontType known
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false
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0 eq { /Identity-H } { /Identity-V } ifelse
exch 1 array astore composefont pop
} {
pdfMakeFont16
} ifelse
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% graphics state operators
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/Q { end grestore } def
/cm { concat } def
/d { setdash } def
/i { setflat } def
/j { setlinejoin } def
/J { setlinecap } def
/M { setmiterlimit } def
/w { setlinewidth } def
% color operators
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/pdfLastFill true def /pdfLastStroke false def } def
/G { dup 1 array astore /pdfStroke exch def setgray
/pdfLastStroke true def /pdfLastFill false def } def
/rg { 3 copy 3 array astore /pdfFill exch def setrgbcolor
/pdfLastFill true def /pdfLastStroke false def } def
/RG { 3 copy 3 array astore /pdfStroke exch def setrgbcolor
/pdfLastStroke true def /pdfLastFill false def } def
/k { 4 copy 4 array astore /pdfFill exch def setcmykcolor
/pdfLastFill true def /pdfLastStroke false def } def
/K { 4 copy 4 array astore /pdfStroke exch def setcmykcolor
/pdfLastStroke true def /pdfLastFill false def } def
/ck { 6 copy 6 array astore /pdfFill exch def
findcmykcustomcolor exch setcustomcolor
/pdfLastFill true def /pdfLastStroke false def } def
/CK { 6 copy 6 array astore /pdfStroke exch def
findcmykcustomcolor exch setcustomcolor
/pdfLastStroke true def /pdfLastFill false def } def
% path segment operators
/m { moveto } def
/l { lineto } def
/c { curveto } def
/re { 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto
neg 0 rlineto closepath } def
/h { closepath } def
% path painting operators
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@endspecial 19 1648 a Fw(Fig.)g(3.)g(Decomp)r(osing)f(double)h(c)n
(hain)f(pseudo-triangulations.)0 1807 y Fo(\015ing)31
b(the)h Fm(i)22 b Fo(+)g(1)31 b(pseudo-triangles)f(of)h
Fm(T)1312 1819 y Fh(B)1400 1807 y Fo(inciden)n(t)g(to)0
1907 y(the)21 b(b)r(ottom)g(and)f(the)h Fm(j)15 b Fo(+)10
b(1)21 b(of)f Fm(T)1035 1919 y Fh(C)1111 1907 y Fo(inciden)n(t)h(to)f
(the)h(top.)0 2036 y Fp(Theorem)k(8)48 b Fn(L)l(et)17
b Fm(V)36 b Fn(and)17 b Fm(W)29 b Fn(b)l(e)18 b(subsets)e(of)i(the)f
(top)h(and)0 2136 y(b)l(ottom)k(interior)h(p)l(oints.)f(F)-6
b(or)22 b(e)l(ach)h Fm(V)1216 2106 y Ff(0)1263 2136 y
Fj(\032)f Fm(V)41 b Fn(and)22 b Fm(W)1682 2106 y Ff(0)1729
2136 y Fj(\032)0 2247 y Fm(W)37 b Fn(let)25 b Fm(t)257
2207 y Fh(V)t(;W)257 2271 y(V)310 2255 y Fc(0)333 2271
y Fh(;W)424 2255 y Fc(0)473 2247 y Fo(=)561 2179 y Fd(\000)599
2209 y Fh(l)p Ff(\000j)p Fh(V)15 b Ff(n)p Fh(V)833 2184
y Fc(0)856 2209 y Ff(j)p Fi(+)p Fh(m)p Ff(\000j)p Fh(W)9
b Ff(n)p Fh(W)1234 2184 y Fc(0)1256 2209 y Ff(j)p Fi(+2)799
2277 y Fh(l)p Ff(\000j)p Fh(V)15 b Ff(n)p Fh(V)1033 2260
y Fc(0)1056 2277 y Ff(j)p Fi(+1)1360 2179 y Fd(\001)1398
2247 y Fn(.)25 b(Then:)0 2431 y Fj(j)p Fn(PT)150 2443
y Fh(V)14 b Ff([)p Fh(W)324 2431 y Fo(\()p Fm(A)p Fo(\))p
Fj(j)24 b Fo(=)620 2353 y Fd(X)584 2526 y Fg(V)630 2514
y Fc(0)653 2526 y(\032)p Fg(V)584 2579 y(W)645 2567 y
Fc(0)667 2579 y(\032)p Fg(W)790 2431 y Fm(t)820 2392
y Fh(V)t(;W)820 2456 y(V)874 2439 y Fc(0)896 2456 y Fh(;W)987
2439 y Fc(0)1014 2431 y Fj(j)p Fn(PPT)1220 2443 y Fh(V)1274
2427 y Fc(0)1300 2431 y Fo(\()p Fm(B)t Fo(\))p Fj(jj)p
Fn(PPT)1661 2443 y Fh(W)1732 2427 y Fc(0)1759 2431 y
Fo(\()p Fm(C)6 b Fo(\))p Fj(j)p Fm(:)0 2702 y Fp(Corollary)25
b(9)48 b Fn(If)16 b(Conje)l(ctur)l(e)g(5)g(holds,)i(then)d(the)h
(double)0 2802 y(chain)26 b(satis\014es)f(Conje)l(ctur)l(e)g(1.)83
2931 y Fo(F)-7 b(or)22 b(p)r(oin)n(ted)h(pseudo-triangulations)e(of)h
(the)h(double)0 3031 y(c)n(hain,)h(Theorem)g(8)h(sa)n(ys)e(that:)57
3253 y Fj(j)p Fn(PT)206 3265 y Fh(A)256 3273 y Fg(I)294
3253 y Fo(\()p Fm(A)p Fo(\))p Fj(j)h Fo(=)604 3149 y
Fh(l)554 3174 y Fd(X)561 3351 y Fh(i)p Fi(=0)719 3149
y Fh(m)688 3174 y Fd(X)691 3351 y Fh(j)s Fi(=0)822 3136
y Fd(\022)883 3197 y Fm(i)18 b Fo(+)g Fm(j)23 b Fo(+)c(2)953
3310 y Fm(i)f Fo(+)g(1)1195 3136 y Fd(\023)1256 3253
y Fm(a)p Fo(\()p Fm(l)r(;)c(i)p Fo(\))p Fm(a)p Fo(\()p
Fm(m;)g(j)5 b Fo(\))p Fm(;)0 3486 y Fo(where)28 b Fm(a)p
Fo(\()p Fj(\001)p Fm(;)14 b Fj(\001)p Fo(\))29 b(is)g(as)f(in)h(the)g
(previous)f(section.)g(The)h(se-)0 3585 y(quence)c(for)f
Fm(l)g Fo(=)f Fm(m)i Fo(is)156 3729 y(2)p Fm(;)14 b Fo(38)p
Fm(;)g Fo(1476)p Fm(;)g Fo(81310)p Fm(;)g Fo(54)o(95)o(27)o(6)p
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Fn(\).)24 b(Then:)120 4896 y Fo(\012\(12)296 4861 y Fh(n)340
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1134 y(Scienc)l(e)35 b(2748,)h(Pr)l(o)l(c.)h(8th)e(International)h
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2196 y(geo)r(desic)35 b(triangulations.)57 b Fs(J.)34
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b(.)58 b(Coun)n(ting)36 b(triangulations)g(of)2127 2467
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2926 y([9])59 b(D.)45 b(Orden)h(and)h(F.)e(San)n(tos.)89
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b Fw(,)42 b(accepted)d(in)2127 3175 y Fs(Discr)l(ete)24
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2127 3363 y(graphs.)40 b Fs(Comput.)29 b(Ge)l(om.)g(The)l(ory)f(Appl.)h
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y([11])24 b(M.)29 b(P)n(o)r(cc)n(hiola)h(and)g(G.)f(V)-6
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3633 y(visibilit)n(y)101 b(complexes)j(via)e(pseudo-triangulations.)
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3904 y(Coun)n(ting)30 b(triangulations)f(and)f(pseudo-triangulations)i
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4590 y(Com)n(binatorics,)17 b(Springer)g(V)-6 b(erlag,)17
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(D.)f(T\023)-35 b(oth.)40 b(Allo)r(cating)28 b(v)n(ertex)h
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5237 y([16])d(I.)30 b(Strein)n(u.)45 b(A)29 b(com)n(binatorial)h
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5403 y(F)n(OCS)26 b Fw(\(2000\))g(443{453.)p eop end
%%Trailer
userdict /end-hook known{end-hook}if
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