Thomas. Lectures in Geometric Combinatorics

《Thomas. Lectures in Geometric Combinatorics》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

1、LecturesinGeometricCombinatoricsRekhaR.ThomasDepartmentofMathematics,UniversityofWashing-ton,Seattle,WA98195E-mailaddress:thomas@math.washington.edu1991MathematicsSubjectClassication.Primary52-01;Secondary13-01TheauthorwassupportedinpartbygrantsDMS-0100141andDMS-0401047fromtheNationalScienceFound

2、ation.Abstract.ThefourteenlecturesinthisbookwerepreparedfortheadvancedundergraduatecourseattheParkCityMath-ematicsInstituteonGeometricCombinatoricsinJuly2004.Theybeginwiththebasicsofpolytopetheorywithanem-phasisongeometryviathetheoryofSchlegelandGaledia-grams.Thelecturesleaduptosecondaryandstatepo

3、lytopesarisingfrompointcongurations.Thesepolytopesarerela-tivelyrecentconstructsthathaveconnectionstoseveralpartsofmathematicssuchascombinatorics,commutativealgebra,algebraicgeometryandsymplecticgeometry.Thetreatmenthereconstructsthemfromscratchandfocusesontheirgeo-metriccombinatorics.Thisbookism

4、eanttobeaccessibletoundergraduateswithabackgroundinlinearalgebra.ContentsPrefaceviiChapter1.AbstractAlgebra:Groups,RingsandFields1Chapter2.ConvexPolytopes:DenitionsandExamples7Chapter3.FacesofPolytopes15Chapter4.SchlegelDiagrams25Chapter5.GaleDiagrams37Chapter6.BizarrePolytopes47Chapter7.Triangul

5、ationsofPointCongurations57Chapter8.TheSecondaryPolytope73Chapter9.ThePermutahedron85Chapter10.AbstractAlgebra:PolynomialRings93Chapter11.Gr•obnerbasesI101Chapter12.Gr•obnerbasesII111Chapter13.InitialComplexesofToricIdeals117vviContentsChapter14.StatePolytopesofToricIdeals127Bibliography139Index1

6、41PrefaceTheselectureswerepreparedfortheadvancedundergraduatecourseattheParkCityMathematicsInstituteinGeometricCombinatoricsinJuly2004.Manythankstotheorganizersoftheundergradu-ateprogram,BillBarkerandRogerHowe,forinvitingmetoteachthiscourse.IalsowishtothankEzraMiller,VicReinerandBerndSturmfelswhoc

7、oordinatedthegraduateresearchprogramatPCMI,fortheirsupport.EdwinO'Sheaconductedallthetutorialsatthecourseandwroteseveraloftheexercisesseenintheselectures.Ed-winwasahugehelpinthepreparationoftheselecturesfromthebe