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1、ThispageintentionallyleftblankP1:...CUUS456-FMcuus456-Kung9780521883894November28,200812:21Combinatorics:TheRotaWayGian-CarloRotawasoneofthemostoriginalandcolorfulmathematiciansofthetwentiethcentury.Hisworkonthefoundationsofcombinatoricsfocusedonrevealingthealgeb
2、raicstructuresthatliebehinddiversecombinatorialareasandcreatedanewareaofalgebraiccombinatorics.Hisgraduatecoursesinfluencedgenerationsofstudents.Writtenbytwoofhisformerstudents,thisbookisbasedonnotesfromhiscoursesandonpersonaldiscussionswithhim.Topicsincludesetsan
3、dvaluations,partiallyor-deredsets,distributivelattices,partitionsandentropy,matchingtheory,freematrices,doublystochasticmatrices,Mobiusfunctions,chainsandantichains,Spernertheory,¨commutingequivalencerelationsandlinearlattices,modularandgeometriclattices,valuatio
4、nrings,generatingfunctions,umbralcalculus,symmetricfunctions,Baxteralgebras,unimodalityofsequences,andlocationofzerosofpolynomials.Manyexer-cisesandresearchproblemsareincludedandunexploredareasofpossibleresearcharediscussed.Thisbookshouldbeontheshelfofallstudents
5、andresearchersincombinatoricsandrelatedareas.josephp.s.kungisaprofessorofmathematicsattheUniversityofNorthTexas.Heiscurrentlyaneditor-in-chiefofAdvancesinAppliedMathematics.gian-carlorota(1932–1999)wasaprofessorofappliedmathematicsandnaturalphilosophyattheMassach
6、usettsInstituteofTechnology.HewasamemberoftheNa-tionalAcademyofScience.Hewasawardedthe1988SteelePrizeoftheAmericanMath-ematicalSocietyforhis1964paper“OntheFoundationsofCombinatorialTheoryI.TheoryofMobiusFunctions.”Hewasafoundingeditorof¨JournalofCombinatorialTheo
7、ry.catherineh.yanisaprofessorofmathematicsatTexasA&MUniversity.Priortothat,shewasaCourantInstructoratNewYorkUniversityandaSloanFellow.iP1:...CUUS456-FMcuus456-Kung9780521883894November28,200812:21iiP1:...CUUS456-FMcuus456-Kung9780521883894November28,200812:21Camb
8、ridgeMathematicalLibraryCambridgeUniversityPresshasalongandhonorablehistoryofpublishinginmathematicsandcountsmanyclassicsofthemathematicalliteraturewithinitsli
