%!PS-Adobe-2.0 %%Creator: dvips(k) 5.92a Copyright 2002 Radical Eye Software %%Title: w2.dvi %%Pages: 7 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentFonts: CMBX12 CMSY10 CMR10 CMMI10 CMR12 MSBM10 CMMI12 CMR7 %%+ CMMI7 CMEX10 LCIRCLE10 CMSY7 CMTI12 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips -o w2.ps w2.dvi %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2005.12.07:1748 %%BeginProcSet: texc.pro %! /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 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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 /.notdef put readonly def /FontBBox{-15 -951 1252 782}readonly def /UniqueID 5000817 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: LCIRCLE10 %!PS-AdobeFont-1.1: LCIRCLE10 1.001 %%CreationDate: 1992 Oct 23 20:21:59 %%RevisionDate: 2001 Jun 05 20:21:59 % Copyright (C) 1997, 2001 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.001) readonly def /Notice (Copyright (C) 1997, 2001 American Mathematical Society. All Rights Reserved) readonly def /FullName (LCIRCLE10) readonly def /FamilyName (LaTeX) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /LCIRCLE10 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 115 /a115 put readonly def /FontBBox{-2000 -2000 2040 2040}readonly def /UniqueID 5011942 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 8 /braceleftbig put dup 9 /bracerightbig put dup 26 /braceleftbigg put dup 27 /bracerightbigg put dup 88 /summationdisplay put dup 110 /braceleftBig put dup 111 /bracerightBig put readonly def /FontBBox{-24 -2960 1454 772}readonly def /UniqueID 5000774 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 /.notdef put readonly def /FontBBox{-29 -960 1116 775}readonly def /UniqueID 5000820 def currentdict end currentfile eexec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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 0 /.notdef 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 0 /.notdef put readonly def /FontBBox{-27 -250 1122 750}readonly def /UniqueID 5000790 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5CF5B8CABB9FFC6CC3F1E9AE32F234EB60FE7D E34995B1ACFF52428EA20C8ED4FD73E3935CEBD40E0EAD70C0887A451E1B1AC8 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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 0 /.notdef put readonly def /FontBBox{-30 -250 1026 750}readonly def /UniqueID 5087386 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE D919C2DDD26BDC0D99398B9F4D03D6A8F05B47AF95EF28A9C561DBDC98C47CF5 5250011D19E9366EB6FD153D3A100CAA6212E3D5D93990737F8D326D347B7EDC 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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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Mathematical Society. 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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 0 /.notdef put readonly def /FontBBox{-32 -250 1048 750}readonly def /UniqueID 5087385 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE D919C2DDD26BDC0D99398B9F4D03D5993DFC0930297866E1CD0A319B6B1FD958 9E394A533A081C36D456A09920001A3D2199583EB9B84B4DEE08E3D12939E321 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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 0 /.notdef put readonly def /FontBBox{-251 -250 1009 969}readonly def /UniqueID 5000793 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5CF7158F1163BC1F3352E22A1452E73FECA8A4 87100FB1FFC4C8AF409B2067537220E605DA0852CA49839E1386AF9D7A1A455F 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%%BeginSetup %%Feature: *Resolution 600dpi TeXDict begin %%PaperSize: A4 end %%EndSetup %%Page: 1 1 TeXDict begin 1 0 bop 825 573 a Fo(On)44 b(parameters)j(sets)e(of)g (algebras)i Fn(P)2771 591 y Fm(\000)p Fl(;\037;\015)716 722 y Fo(when)e Fk(\000)g Fo(is)g(an)g(extended)g(Dynkin)g(diagram)1296 1344 y(Kost)l(y)l(an)l(t)l(yn)i(Y)-11 b(usenk)l(o)964 1966 y(Kiev,)46 b(Institute)g(of)f(Mathematics)1852 5637 y Fj(1)p eop end %%Page: 2 2 TeXDict begin 2 1 bop 404 573 a Fk(Consider)37 b Fn(\003)p Fk(-algebras)g(related)g(to)h(graphs)432 971 y Fn(P)515 989 y Fm(\000)p Fl(;\037;\015)750 971 y Fk(=)33 b Fi(C)p Fn(h)p Fh(p)1065 909 y Fm(\(1\))1065 1003 y(1)1176 971 y Fh(;)20 b(:)g(:)g(:)e(p)1445 922 y Fm(\(1\))1445 1001 y Fl(m)1518 1013 y Fg(1)1559 971 y Fh(;)i(:)g(:)g(:)e(p)1828 909 y Fm(\()p Fl(n)p Fm(\))1828 1003 y(1)1946 971 y Fh(;)i(:)g(:)g(:)e (p)2215 922 y Fm(\()p Fl(n)p Fm(\))2215 1001 y Fl(m)2288 1013 y Ff(n)2337 971 y Fn(j)p Fh(p)2429 909 y Fm(\()p Fl(k)s Fm(\))2429 1004 y Fl(i)2577 971 y Fk(=)33 b Fh(p)2760 909 y Fm(\()p Fl(k)s Fm(\)2)2760 1004 y Fl(i)2949 971 y Fk(=)g Fh(p)3132 909 y Fm(\()p Fl(k)s Fm(\))p Fe(\003)3132 1004 y Fl(i)3288 971 y Fh(;)1730 1099 y Fl(n)1668 1135 y Fd(X)1687 1389 y Fl(i)p Fm(=1)1897 1097 y Fl(m)1970 1109 y Ff(i)1861 1135 y Fd(X)1871 1392 y Fl(k)s Fm(=1)2053 1248 y Fh(\013)2128 1186 y Fm(\()p Fl(i)p Fm(\))2127 1284 y Fl(k)2226 1248 y Fh(p)2285 1186 y Fm(\()p Fl(i)p Fm(\))2285 1284 y Fl(k)2415 1248 y Fk(=)g Fh(\015)7 b(e;)20 b(p)2773 1186 y Fm(\()p Fl(i)p Fm(\))2773 1281 y Fl(j)2869 1248 y Fh(p)2928 1186 y Fm(\()p Fl(i)p Fm(\))2928 1284 y Fl(k)3059 1248 y Fk(=)33 b(0)p Fn(i)p Fh(:)404 1595 y Fk(Suc)m(h)39 b(algebras)1852 5637 y Fj(2)p eop end %%Page: 3 3 TeXDict begin 3 2 bop 1059 573 a Fo(2.)60 b(Extended)46 b(Dynkin)e(graphs)404 959 y Fk(In)k(this)f(talk)f(w)m(e)h(consider)g Fn(P)1771 976 y Fm(\000)p Fl(;\037;\015)2021 959 y Fk(algebras)f (related)g(to)h(extended)257 1108 y(Dynkin)39 b(graphs.)1478 1664 y Fc(s)216 b(s)g(s)1727 1415 y(s)1727 1913 y(s)p 1478 1666 250 4 v 1727 1666 V 1725 1664 4 250 v 1725 1913 V 1517 1450 a Fk(~)1489 1480 y Fh(D)1586 1498 y Fm(4)1063 2760 y Fc(s)299 b(s)g(s)g(s)g(s)1727 2511 y(s)1727 2262 y(s)p 1063 2761 333 4 v 1395 2761 V 1727 2761 V 2059 2761 V 1725 2511 4 250 v 1725 2760 V 1190 2629 a Fk(~)1163 2659 y Fh(E)1250 2677 y Fm(6)731 3536 y Fc(s)g(s)g(s)g(s)g(s) g(s)g(s)1727 3287 y(s)p 731 3538 333 4 v 2391 3538 V 1063 3538 V 1395 3538 V 1727 3538 V 2059 3538 V 1725 3536 4 250 v 1190 3322 a Fk(~)1163 3352 y Fh(E)1250 3370 y Fm(7)1063 4312 y Fc(s)g(s)g(s)g(s)g(s)g(s)g(s)g(s)1727 4063 y(s)p 2723 4314 333 4 v 3055 4314 V 2391 4314 V 1063 4314 V 1395 4314 V 1727 4314 V 2059 4314 V 1725 4312 4 250 v 1190 4098 a Fk(~)1163 4128 y Fh(E)1250 4146 y Fm(8)1852 5637 y Fj(3)p eop end %%Page: 4 4 TeXDict begin 4 3 bop 1302 573 a Fo(3.)60 b(Co)l(xeter)47 b(functors)404 959 y Fk(The)53 b(p)s(o)m(w)m(erful)f(to)s(ol)g(to)h(in) m(v)m(estigate)d(algebras)i Fn(P)2710 976 y Fm(\000)p Fl(;\037;\015)2966 959 y Fk(is)i(Co)m(xeter)257 1108 y(functors.)d(There)38 b(are)g(t)m(w)m(o)f(functors)h(of)g(linear)1171 1357 y Fh(S)i Fk(:)33 b(Rep)p Fn(P)1635 1375 y Fm(\000)p Fl(;\037;\015)1870 1357 y Fn(!)g Fk(Rep)p Fn(P)2309 1375 y Fm(\000)p Fl(;\037)2436 1351 y Fb(\003)2474 1375 y Fl(;\015)2549 1357 y Fh(;)474 1623 y(\037)547 1574 y Fe(\003)626 1623 y Fk(=)g(\()p Fh(\015)g Fn(\000)26 b Fh(\013)1084 1574 y Fm(\(1\))1083 1653 y Fl(m)1156 1665 y Fg(1)1198 1623 y Fh(;)20 b(:)g(:)g(:)e(;)i(\015)32 b Fn(\000)27 b Fh(\013)1749 1561 y Fm(\(1\))1748 1655 y(1)1859 1623 y Fk(;)20 b Fh(:)g(:)g(:)e Fk(;)i Fh(\015)32 b Fn(\000)27 b Fh(\013)2410 1574 y Fm(\()p Fl(n)p Fm(\))2409 1653 y Fl(m)2482 1665 y Ff(n)2531 1623 y Fh(;)20 b(:)g(:)g(:)e(;)i (\015)32 b Fn(\000)27 b Fh(\013)3082 1561 y Fm(\()p Fl(n)p Fm(\))3081 1655 y(1)3201 1623 y Fk(\))p Fh(;)257 1827 y Fk(and)39 b(h)m(yp)s(erb)s(olic)1164 2076 y Fh(T)49 b Fk(:)33 b(Rep)p Fn(P)1634 2094 y Fm(\000)p Fl(;\037;\015)1869 2076 y Fn(!)g Fk(Rep)p Fn(P)2308 2094 y 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Fm(\))2162 2589 y Fl(m)2235 2601 y Ff(n)2311 2560 y Fn(\000)g Fh(\015)7 b Fk(;)404 2999 y(These)37 b(t)m(w)m(o)f(functors)g(are)h(b)s(eing)g (applied)g(t)m(wice)f(equal)g(to)h(iden)m(tit)m(y)-10 b(,)257 3149 y(therefore)37 b(w)m(e)i(use)g(their)f(comp)s(osition)e (\010)2142 3105 y Fm(+)2243 3149 y Fk(=)e Fh(S)f Fn(\016)26 b Fh(T)16 b Fk(.)1852 5637 y Fj(4)p eop end %%Page: 5 5 TeXDict begin 5 4 bop 1187 573 a Fo(4.)61 b(In)l(v)-7 b(arian)l(t)46 b(functionals)404 959 y Fk(Let)40 b Fh(!)t Fk(\()p Fh(\037)p Fk(\))h(b)s(e)g(a)f(p)s(ositiv)m(e)f(functional)f(on) i(\000.)57 b(W)-10 b(e)42 b(sa)m(y)e(that)f Fh(!)t Fk(\()p Fh(\037)p Fk(\))i(is)257 1108 y(an)e(in)m(v)-7 b(arian)m(t)36 b(functional)g(if)j(the)f(follo)m(wing)e(conditions)h(holds:)1182 1357 y Fh(S)j Fk(:)33 b(\()p Fh(\037;)20 b(!)t Fk(\()p Fh(\037)p Fk(\)\))31 b Fn(7\000)-19 b(!)32 b Fk(\()p Fh(\037)2196 1308 y Fe(0)2223 1357 y Fh(;)20 b(!)t Fk(\()p Fh(\037)2472 1308 y Fe(0)2499 1357 y Fk(\)\))p Fh(;)1130 1531 y(T)50 b Fk(:)32 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y(!)349 3052 y Fm(~)330 3074 y Fl(E)391 3086 y Fg(8)433 3038 y Fk(\()p Fh(\037)p Fk(\))33 b(=)765 2957 y(1)p 765 3011 V 765 3120 a(6)833 3038 y(\()p Fh(\013)954 2976 y Fm(\(1\))953 3070 y(1)1091 3038 y Fk(+)26 b Fh(\013)1283 2976 y Fm(\(1\))1282 3070 y(2)1420 3038 y Fk(+)h Fh(\013)1613 2976 y Fm(\(1\))1612 3070 y(3)1750 3038 y Fk(+)g Fh(\013)1943 2976 y Fm(\(1\))1942 3070 y(4)2080 3038 y Fk(+)f Fh(\013)2272 2976 y Fm(\(1\))2271 3070 y(5)2409 3038 y Fk(+)h(2)p Fh(\013)2661 2976 y Fm(\(2\))2660 3070 y(1)2797 3038 y Fk(+)g(2)p Fh(\013)3049 2976 y Fm(\(2\))3048 3070 y(2)3186 3038 y Fk(+)f(3)p Fh(\013)3437 2976 y Fm(\(3\))3436 3070 y(1)3547 3038 y Fk(\))p Fh(:)404 3507 y Fk(In)k(case)g(where)f Fh(\015)40 b Fk(=)33 b Fh(!)1407 3525 y Fm(\000)1463 3507 y Fk(\()p Fh(\037)p Fk(\))c(the)h(algebras)e Fn(P)2380 3528 y Fm(\000)p Fl(;\037;!)2582 3540 y Fg(\000)2627 3528 y Fm(\()p Fl(\037)p Fm(\))2777 3507 y Fk(are)i(PI-algebra)257 3657 y(and)c(their)f(irreducible)e(represen)m(tations)g(are)i(of)h 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Fm(2)2973 4504 y Fk(\()p Fh(n)p Fk(\)\))p Fh(;)404 4753 y Fk(where)55 b Fh(\025)63 b Fk(=)f Fh(!)1116 4771 y Fm(\000)1172 4753 y Fk(\()p Fh(\037)p Fk(\))38 b Fn(\000)g Fh(\015)7 b Fk(,)59 b Fh(t)k Fk(=)f([)1986 4706 y Fl(n)p 1967 4725 89 5 v 1967 4794 a(k)2010 4806 y Fg(\000)2065 4753 y Fk(],)d Fh(k)2270 4767 y Fm(~)2251 4788 y Fl(D)2320 4800 y Fg(4)2424 4753 y Fk(=)j(2)p Fh(;)20 b(k)2769 4767 y Fm(~)2750 4788 y Fl(E)2811 4800 y Fg(6)2914 4753 y Fk(=)62 b(6)p Fh(;)20 b(k)3259 4767 y Fm(~)3240 4788 y Fl(E)3301 4800 y Fg(7)3404 4753 y Fk(=)257 4902 y(12)p Fh(;)g(k)508 4916 y Fm(~)489 4937 y Fl(E)550 4949 y Fg(8)624 4902 y Fk(=)33 b(30.)47 b(Notice)26 b(that)g(the)i(v)m(ector)d Fh(v)2131 4920 y Fm(1)2177 4902 y Fk(\()p Fh(t;)20 b(n)p Fk(\))26 b(and)h(n)m(um)m(b)s(ers)g Fh(v)3194 4920 y Fm(2)3240 4902 y Fk(\()p Fh(t;)20 b(n)p Fk(\))257 5051 y(dep)s(ends)38 b(on)f Fh(\037)g Fk(and)g(indep)s(enden)m(t)g(on)f Fh(\025)i Fk(and)f(the)g(comp)s(onen)m(ts)e(of)i(the)257 5201 y(v)m(ector)h Fh(w)693 5219 y Fm(1)738 5201 y Fk(\()p Fh(t;)20 b(n)p Fk(\))38 b(are)g(strictly)e(increasing)h(with)h(n.)1852 5637 y Fj(5)p eop end %%Page: 6 6 TeXDict begin 6 5 bop 1000 573 a Fo(6.)60 b(Description)46 b(of)f(the)g(set)h Fk(\006)2587 587 y Fm(~)2568 608 y Fl(D)2637 620 y Fg(4)2674 608 y Fl(;\037)404 959 y Fk(Using)38 b(considered)g(tec)m(hnique)f(w)m(e)i(ha)m(v)m(e)f(describ)s(ed)g(the)h (set)g(\006)3281 973 y Fm(~)3262 994 y Fl(D)3331 1006 y Fg(4)3367 994 y Fl(;\037)257 1191 y Fo(Lemma)54 b(1.)45 b Fa(The)j(set)f Fk(\006)1429 1205 y Fm(~)1410 1226 y Fl(D)1479 1238 y Fg(4)1516 1226 y Fl(;\037)1643 1191 y Fa(c)-6 b(ontains)47 b(the)h(in\014nity)e(series)i Fk(\006)3148 1209 y Fe(1)3283 1191 y Fa(with)257 1340 y(limit)h(p)-6 b(oint)856 1293 y Fl(\013)p 856 1313 54 5 v 862 1382 a Fm(2)969 1340 y Fa(and)48 b(the)h(\014nite)f(series)h Fk(\006)2137 1358 y Fm(0)2182 1340 y Fa(.)76 b(This)48 b(two)h(series)g(ar)-6 b(e)49 b(de-)257 1490 y(scrib)-6 b(e)g(d)41 b(by)h(the)f(fol)6 b(lowing)40 b(rule:)357 1722 y(1.)48 b(when)41 b Fh(\013)874 1740 y Fm(2)947 1722 y Fk(+)26 b Fh(\013)1138 1740 y Fm(3)1218 1722 y Fh(>)33 b(\013)1416 1740 y Fm(1)1489 1722 y Fk(+)26 b Fh(\013)1680 1740 y Fm(4)1768 1722 y Fa(then)41 b Fk(\006)2113 1740 y Fe(1)2233 1722 y Fk(=)2357 1625 y Fd(\010)2437 1675 y Fl(\013)p 2437 1695 V 2443 1764 a Fm(2)2527 1722 y Fn(\000)2657 1673 y Fl(\013)2710 1685 y Fg(1)p 2657 1695 92 5 v 2657 1764 a Fm(2)p Fl(n)2758 1722 y Fn(j)p Fh(n)33 b Fn(2)g Fi(N)3093 1625 y Fd(\011)3205 1722 y Fa(and)501 1910 y Fk(\006)586 1928 y Fm(0)665 1910 y Fk(=)789 1777 y Fd(n)879 1863 y Fl(\013)p 879 1882 54 5 v 885 1951 a Fm(2)969 1910 y Fn(\000)1125 1860 y Fl(\013)p Fe(\000)p Fm(2)p Fl(\013)1338 1872 y Fg(4)p 1098 1882 304 5 v 1098 1951 a Fm(2\(2)p Fl(n)p Fe(\000)p Fm(1\))1412 1910 y Fn(j)p Fh(n)g(<)1939 1863 y Fm(1)p 1682 1882 556 5 v 1682 1951 a Fl(\013)1735 1963 y Fg(2)1772 1951 y Fm(+)p Fl(\013)1890 1963 y Fg(3)1927 1951 y Fe(\000)p Fl(\013)2045 1963 y Fg(1)2082 1951 y Fe(\000)p Fl(\013)2200 1963 y Fg(4)2247 1910 y Fh(;)20 b(n)33 b Fn(2)g Fi(N)2602 1777 y Fd(o)357 2216 y Fa(2.)48 b(when)h Fh(\013)882 2234 y Fm(2)960 2216 y Fk(+)32 b Fh(\013)1157 2234 y Fm(3)1250 2216 y Fh(<)47 b(\013)1462 2234 y Fm(1)1540 2216 y Fk(+)33 b Fh(\013)1738 2234 y Fm(4)1833 2216 y Fa(then)49 b Fk(\006)2186 2234 y Fe(1)2319 2216 y Fk(=)2457 2084 y Fd(n)2547 2169 y Fl(\013)p 2547 2189 54 5 v 2553 2258 a Fm(2)2637 2216 y Fn(\000)2793 2167 y Fl(\013)p Fe(\000)p Fm(2)p Fl(\013)3006 2179 y Fg(4)p 2767 2189 304 5 v 2767 2258 a Fm(2\(2)p Fl(n)p Fe(\000)p Fm(1\))3080 2216 y Fn(j)p Fh(n)33 b Fn(2)g Fi(N)3415 2084 y Fd(o)501 2385 y Fa(and)501 2535 y Fk(\006)586 2553 y Fm(0)665 2535 y Fk(=)789 2402 y Fd(n)879 2488 y Fl(\013)p 879 2507 54 5 v 885 2576 a Fm(2)969 2535 y Fn(\000)1099 2485 y Fl(\013)1152 2497 y Fg(1)p 1098 2507 92 5 v 1098 2576 a Fm(2)p Fl(n)1199 2535 y Fn(j)p Fh(n)h(<)1727 2488 y Fm(1)p 1470 2507 556 5 v 1470 2576 a Fl(\013)1523 2588 y Fg(1)1560 2576 y Fm(+)p Fl(\013)1678 2588 y Fg(4)1715 2576 y Fe(\000)p Fl(\013)1833 2588 y Fg(2)1870 2576 y Fe(\000)p Fl(\013)1988 2588 y Fg(3)2035 2535 y Fh(;)20 b(n)32 b Fn(2)h Fi(N)2389 2402 y Fd(o)357 2806 y Fa(3.)48 b(when)g Fh(\013)881 2824 y Fm(2)960 2806 y Fk(+)32 b Fh(\013)1157 2824 y Fm(3)1250 2806 y Fk(=)47 b Fh(\013)1462 2824 y Fm(1)1540 2806 y Fk(+)32 b Fh(\013)1737 2824 y Fm(4)1832 2806 y Fa(then)48 b Fk(\006)2184 2824 y Fe(1)2318 2806 y Fk(=)2456 2709 y Fd(\010)2536 2759 y Fl(\013)p 2536 2778 54 5 v 2542 2847 a Fm(2)2626 2806 y Fn(\000)2755 2756 y Fl(\013)2808 2768 y Fg(1)p 2755 2778 91 5 v 2775 2847 a Fl(n)2855 2806 y Fn(j)p Fh(n)34 b Fn(2)f Fi(N)3191 2709 y Fd(\011)3310 2806 y Fa(and)501 2955 y Fk(\006)586 2973 y Fm(0)665 2955 y Fk(=)g Fi(?)p Fa(.)257 3187 y Fo(Theorem)45 b(1.)257 3437 y Fk(\006)361 3451 y Fm(~)342 3472 y Fl(D)411 3484 y Fg(4)448 3472 y Fl(;\037)527 3437 y Fn(\\)p Fk([0;)20 b Fh(\013)q(=)p Fk(2\))30 b(=)k(\006)1231 3454 y Fe(1)1317 3437 y Fn([)p Fk(\006)1482 3454 y Fm(0)1527 3437 y Fn([)p Fk(\006)1692 3454 y Fm(1)1737 3437 y Fn([)p Fk(\006)1902 3387 y Fl(i)1902 3466 y Fm(2)1947 3437 y Fn([)p Fk(\006)2112 3454 y Fm(3)2157 3437 y Fn([)p Fk(\006)2322 3454 y Fm(4)2367 3437 y Fn([)p Fk(\006)2532 3379 y Fl(j)2532 3468 y Fm(5)2577 3437 y Fh(;)139 b(i)33 b Fk(=)g(2)p Fh(;)20 b Fk(3)p Fh(;)g Fk(4)p Fh(;)137 b(j)40 b Fk(=)33 b(1)p Fh(;)20 b Fk(2)p Fh(;)g Fk(3)p Fh(;)1852 5637 y Fj(6)p eop end %%Page: 7 7 TeXDict begin 7 6 bop 257 573 a Fa(wher)-6 b(e)423 854 y Fk(\006)508 872 y Fm(1)587 854 y Fk(=)711 686 y Fd(\032)811 773 y Fh(\013)p 811 827 76 5 v 819 936 a Fk(2)923 854 y Fn(\000)1256 773 y Fh(\013)p 1052 827 483 5 v 1052 936 a Fk(2\(4)p Fh(n)25 b Fn(\000)i Fk(1\))1545 854 y Fn(j)40 b Fh(n)33 b(<)1995 773 y(\013)2069 791 y Fm(4)p 1855 827 400 5 v 1855 936 a Fk(4)p Fh(\013)1988 954 y Fm(4)2060 936 y Fn(\000)27 b Fh(\013)2265 854 y(;)20 b(n)32 b(<)2584 773 y(\013)c Fn(\000)e Fh(\013)2879 791 y Fm(1)p 2555 827 V 2555 936 a Fh(\013)h Fn(\000)g Fk(4)p Fh(\013)2909 954 y Fm(1)2965 854 y Fh(;)20 b(n)32 b Fn(2)h Fi(N)3319 686 y Fd(\033)3429 854 y Fh(;)257 1138 y Fk(\006)342 1089 y Fl(i)342 1168 y Fm(2)421 1138 y Fk(=)545 1006 y Fd(n)635 1058 y Fh(\013)p 635 1111 76 5 v 643 1220 a Fk(2)746 1138 y Fn(\000)887 1058 y Fh(\013)961 1075 y Fl(i)p 876 1111 129 5 v 876 1220 a Fk(2)p Fh(n)1014 1138 y Fn(j)p Fh(i)h Fk(=)f(2)p Fh(;)20 b Fk(3)p Fh(;)g Fk(4;)27 b Fh(n)33 b(<)2126 1058 y(\013)2200 1075 y Fl(i)p 1825 1111 710 5 v 1825 1220 a Fk(2)p Fh(\013)1958 1238 y Fl(i)2017 1220 y Fk(+)27 b(2)p Fh(\013)2268 1238 y Fm(4)2340 1220 y Fn(\000)g Fh(\013)2545 1138 y(;)20 b(n)33 b(<)2968 1058 y(\013)3042 1075 y Fl(i)p 2835 1111 374 5 v 2835 1220 a Fh(\013)2909 1238 y Fl(i)2968 1220 y Fn(\000)27 b Fh(\013)3162 1238 y Fm(1)1618 1445 y Fh(n)33 b(<)1995 1364 y(\013)2069 1382 y Fl(i)p 1855 1417 388 5 v 1855 1527 a Fk(4)p Fh(\013)1988 1545 y Fl(i)2047 1527 y Fn(\000)27 b Fh(\013)2252 1445 y(;)20 b(n)33 b Fn(2)f Fi(N)2606 1276 y Fd(\033)2716 1445 y Fh(;)139 b(i)34 b Fk(=)f(2)p Fh(;)20 b Fk(3)p Fh(;)g Fk(4)p Fh(;)425 1765 y Fk(\006)510 1783 y Fm(3)589 1765 y Fk(=)713 1596 y Fd(\032)813 1684 y Fh(\013)p 813 1738 76 5 v 821 1847 a Fk(2)924 1765 y Fn(\000)1094 1684 y Fh(\013)28 b Fn(\000)f Fk(2)p Fh(\013)1449 1702 y Fm(1)p 1054 1738 481 5 v 1054 1847 a Fk(2\(2)p Fh(n)e Fk(+)i(1\))1545 1765 y Fn(j)40 b Fh(n)33 b(<)1884 1684 y(\013)28 b Fn(\000)f Fh(\013)2180 1702 y Fm(1)p 1855 1738 400 5 v 1855 1847 a Fh(\013)h Fn(\000)e Fk(4)p Fh(\013)2209 1865 y Fm(1)2265 1765 y Fh(;)20 b(n)32 b(<)2630 1684 y(\013)2704 1702 y Fm(2)2777 1684 y Fk(+)27 b Fh(\013)2969 1702 y Fm(3)p 2555 1738 536 5 v 2555 1847 a Fk(2\()p Fh(\013)2734 1865 y Fm(4)2805 1847 y Fn(\000)g Fh(\013)2999 1865 y Fm(1)3045 1847 y Fk(\))3101 1765 y Fh(;)20 b(n)32 b Fn(2)h Fi(N)3455 1596 y Fd(\033)3565 1765 y Fh(;)425 2085 y Fk(\006)510 2103 y Fm(4)589 2085 y Fk(=)713 1917 y Fd(\032)813 2004 y Fh(\013)p 813 2058 76 5 v 821 2167 a Fk(2)924 2085 y Fn(\000)1257 2004 y Fh(\013)p 1054 2058 481 5 v 1054 2167 a Fk(2\(4)p Fh(n)25 b Fk(+)i(1\))1545 2085 y Fn(j)40 b Fh(n)33 b(<)1884 2004 y(\013)28 b Fn(\000)f Fh(\013)2180 2022 y Fm(4)p 1855 2058 400 5 v 1855 2167 a Fk(4)p Fh(\013)1988 2185 y Fm(4)2060 2167 y Fn(\000)g Fh(\013)2265 2085 y(;)20 b(n)32 b(<)2695 2004 y(\013)2769 2022 y Fm(1)p 2555 2058 V 2555 2167 a Fh(\013)27 b Fn(\000)g Fk(4)p Fh(\013)2909 2185 y Fm(1)2965 2085 y Fh(;)20 b(n)32 b Fn(2)h Fi(N)3319 1917 y Fd(\033)3429 2085 y Fh(;)425 2405 y Fk(\006)510 2356 y Fl(i)510 2435 y Fm(5)589 2405 y Fk(=)713 2237 y Fd(\032)813 2324 y Fh(\013)p 813 2378 76 5 v 821 2487 a Fk(2)924 2405 y Fn(\000)1101 2324 y Fh(\013)28 b Fn(\000)e Fk(2)p Fh(\013)1455 2342 y Fl(i)p 1054 2378 481 5 v 1054 2487 a Fk(2\(2)p Fh(n)f Fk(+)i(1\))1545 2405 y Fn(j)10 b Fh(n)33 b(<)2121 2324 y(\013)2195 2342 y Fm(1)p 1825 2378 712 5 v 1825 2487 a Fh(\013)28 b Fn(\000)e Fk(2)p Fh(\013)2179 2505 y Fl(i)2239 2487 y Fn(\000)g Fk(2)p Fh(\013)2491 2505 y Fm(1)2547 2405 y Fh(;)20 b(n)32 b(<)2977 2324 y(\013)3051 2342 y Fl(i)p 2837 2378 388 5 v 2837 2487 a Fh(\013)27 b Fn(\000)g Fk(4)p Fh(\013)3191 2505 y Fl(i)3234 2405 y Fh(;)1618 2725 y(n)33 b(<)1855 2645 y(\013)28 b Fn(\000)e Fh(\013)2150 2662 y Fm(4)2223 2645 y Fn(\000)h Fh(\013)2417 2662 y Fl(i)p 1855 2698 595 5 v 1891 2807 a Fk(2\()p Fh(\013)2070 2825 y Fm(4)2142 2807 y Fn(\000)f Fh(\013)2335 2825 y Fl(i)2368 2807 y Fk(\))2460 2725 y Fh(;)20 b(n)32 b Fn(2)h Fi(N)27 b Fn([)f(f)p Fk(0)p Fn(g)3126 2557 y Fd(\033)3235 2725 y Fh(;)139 b(i)33 b Fk(=)g(1)p Fh(;)20 b Fk(2)p Fh(;)g Fk(3)p Fh(:)1852 5637 y Fj(7)p eop end %%Trailer userdict /end-hook known{end-hook}if %%EOF

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