This is a multi-part message in MIME format. ---------------0402271222294 Content-Type: text/plain; name="04-51.comments" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="04-51.comments" For later versions of the paper see http:www.ma.utexas.edu/users/radin/papers.html ---------------0402271222294 Content-Type: text/plain; name="04-51.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="04-51.keywords" ground states, densest packing ---------------0402271222294 Content-Type: application/postscript; name="grndstate.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="grndstate.ps" %!PS-Adobe-2.0 %%Creator: dvips(k) 5.92b Copyright 2002 Radical Eye Software %%Title: text33.dvi %%Pages: 8 %%PageOrder: Ascend %%BoundingBox: 0 0 612 792 %%DocumentFonts: CMBX10 CMR10 CMMI10 MSBM10 CMMI7 CMSY10 CMTI10 CMEX10 %%+ CMSY7 CMR7 CMSY5 CMMI5 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips 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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 0 /.notdef put readonly def /FontBBox{21 -944 1448 791}readonly def /UniqueID 5000815 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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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 /.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: 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 2 /bracketleftbig put dup 3 /bracketrightbig put dup 26 /braceleftbigg put dup 80 /summationtext put dup 82 /integraltext put dup 88 /summationdisplay put dup 90 /integraldisplay put dup 104 /bracketleftBig put dup 105 /bracketrightBig put readonly def /FontBBox{-24 -2960 1454 772}readonly def /UniqueID 5000774 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 0 /.notdef put readonly def /FontBBox{-163 -250 1146 969}readonly def /UniqueID 5000828 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE D919C2DDD26BDC0D99398B9F4D03D5993DFC0930297866E1CD0A319B6B1FD958 9E3948FFB0B4E70F212EC976D65099D84E0D37A7A771C3101D6AD26A0513378F 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 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. 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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. 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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. 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 69 /E put dup 82 /R put readonly def /FontBBox{-55 -420 2343 920}readonly def /UniqueID 5031982 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 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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%!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. 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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 0 /.notdef put readonly def /FontBBox{-301 -250 1164 946}readonly def /UniqueID 5000768 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5F00F963068B8B731A88D7740B0DDAED1B3F82 7DB9DFB4372D3935C286E39EE7AC9FB6A9B5CE4D2FAE1BC0E55AE02BFC464378 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Fl(IV.)j(References)174 2671 y Fk([B])48 b(L.)38 b(Bo)m(w)m(en,)h(On)f(the)g(existence)g(of)g(completely)f(saturated)h (pac)m(kings)g(and)g(completely)349 2791 y(reduced)d(co)m(v)m(erings,)f Ff(Ge)-5 b(ometria)35 b(De)-5 b(dic)g(ata)32 b Fl(98)i Fk(\(2003\))e(211-226.)-30 2910 y([BHRS])49 b(L.)41 b(Bo)m(w)m(en,)h (C.)e(Holton,)h(C.)f(Radin)g(and)h(L.)f(Sadun\))i(Uniqueness)f(and)g (symmetry)f(in)349 3030 y(problems)30 b(of)e(optimally)f(dense)k(pac)m (kings.)42 b(Preprin)m(t,)30 b(Univ)m(ersit)m(y)e(of)h(T)-8 b(exas)28 b(at)g(Austin,)349 3149 y(a)m(v)-6 b(ailable)33 b(from)649 3269 y(ftp://ftp.ma.utexas.edu/pub/pap)s(ers/radin/unique.p) s(df)166 3388 y([G])49 b(J.)30 b(Ginibre,)h(On)g(some)f(recen)m(t)h(w)m (ork)e(of)i(Dobrushin,)g(in)f Ff(Syst)m(\022)-48 b(emes)33 b(\022)-51 b(a)32 b(un)h(nombr)-5 b(e)33 b(in\014ni)349 3508 y(de)j(de)-5 b(gr)m(\023)-48 b(es)34 b(de)i(lib)-5 b(ert)m(\023)-48 b(e)p Fk(,)32 b(CNRS,)h(P)m(aris,)g(1969,)f(pp.)45 b(163-175.)102 3628 y([HP])j(O.)36 b(Heilmann)f(and)h(E.)e (Praestgaard,)h(Phase)h(transition)f(of)h(hard)f(hexagons)h(on)f(a)g (tri-)349 3747 y(angular)e(lattice,)f Ff(J.)k(Stat.)45 b(Phys.)f Fl(9)33 b Fk(\(1973\))f(23-44.)149 3867 y([Pi])48 b(A.)24 b(Pippard,)h Ff(The)j(Elements)f(of)f(Classic)-5 b(al)27 b(Thermo)-5 b(dynamics)p Fk(,)26 b(Cam)m(bridge)f(Univ)m(ersit) m(y)349 3986 y(Press,)34 b(Cam)m(bridge,)f(1979,)f(p.)45 b(122.)137 4106 y([Pr])k(C.)29 b(Preston,)h Ff(R)-5 b(andom)32 b(Fields)p Fk(,)e(Lecture)g(Notes)f(in)h(Mathematics,)g(V)-8 b(ol.)28 b(534,)h(Springer-)349 4225 y(V)-8 b(erlag,)32 b(Berlin,)h(1976.)71 4345 y([Ra1])49 b(C.)36 b(Radin,)g(Orbits)h(of)f (orbs:)50 b(sphere)37 b(pac)m(king)f(meets)g(P)m(enrose)h(tilings,)f Ff(A)m(mer.)53 b(Math.)349 4464 y(Monthly)35 b Fl(111)f Fk(\(2004\))e(137-149.)71 4584 y([Ra2])49 b(C.)39 b(Radin,)i(Global)e (Order)h(from)g(Lo)s(cal)e(Sources,)k(Review-Exp)s(ository)c(P)m(ap)s (er,)j Ff(Bul)5 b(l.)349 4703 y(A)m(mer.)46 b(Math.)g(So)-5 b(c.)44 b Fl(25)33 b Fk(\(1991\))f(335-364.)71 4823 y([Ra3])49 b(C.)43 b(Radin,)i(Lo)m(w)e(temp)s(erature)g(and)g(the)g(origin)f(of)h (crystalline)f(symmetry)-8 b(,)44 b Ff(Intl.)72 b(J.)349 4943 y(Mo)-5 b(d.)46 b(Phys.)d Fl(B1)34 b Fk(\(1987\))e(1157-1191.)71 5062 y([Ra4])49 b(C.)33 b(Radin,)g(Symmetries)h(of)f(quasicrystals,)g Ff(J.)i(Stat.)46 b(Phys.)d Fl(95)34 b Fk(\(1999\))e(827-833.)1925 5519 y(6)p eop end %%Page: 7 8 TeXDict begin 7 7 bop 121 100 a Fk([Ro])49 b(R.)29 b(Ro)s(c)m(k)-6 b(afellar,)29 b(Measurable)g(dep)s(endence)j(of)c(con)m(v)m(ex)h(sets)g (and)g(functions)g(on)g(param-)349 219 y(eters,)34 b Ff(J.)h(Math.)46 b(A)m(nal.)g(Appl.)e Fl(28)34 b Fk(\(1969\))e(4-25.) 115 339 y([Ru])50 b(D.)30 b(Ruelle,)g Ff(Statistic)-5 b(al)32 b(Me)-5 b(chanics;)32 b(R)m(igor)-5 b(ous)31 b(R)-5 b(esults)p Fk(,)30 b(Benjamin,)h(New)e(Y)-8 b(ork,)29 b(1969.)189 458 y([S])49 b(R.)39 b(Sc)m(hrader,)j(Ground)e(states)f(in) g(classical)g(lattice)f(systems)h(with)g(hard)g(core,)i Ff(Com-)349 578 y(mun.)47 b(Math.)e(Phys.)f Fl(16)33 b Fk(\(1970\))f(247-264.)172 697 y([T])49 b(A.)38 b(T)-8 b(a)m(ylor,)39 b Ff(Gener)-5 b(al)40 b(The)-5 b(ory)41 b(of)f(F)-8 b(unctions)41 b(and)f(Inte)-5 b(gr)g(ation)p Fk(,)39 b(Blaisdell,)g(W)-8 b(altham,)349 817 y(1965.)142 936 y([W])49 b(P)-8 b(.)45 b(W)-8 b(alters,)48 b Ff(A)m(n)g(Intr)-5 b(o)g(duction)47 b(to)g(Er)-5 b(go)g(dic)45 b(The)-5 b(ory)p Fk(,)49 b(Springer-V)-8 b(erlag,)48 b(New)d(Y)-8 b(ork,)349 1056 y(1982.)1925 5519 y(7)p eop end %%Trailer userdict /end-hook known{end-hook}if %%EOF ---------------0402271222294--