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1、LecturesonIntegerPartitionsHerbertS.WilfUniversityofPennsylvania2PrefaceTheselecturesweredeliveredattheUniversityofVictoria,Victoria,B.C.,Canada,inJuneof2000,undertheauspicesofthePaci cInstitutefortheMathematicalSciences.Myoriginalintentwastodescribethesequenceofdevelopmentswhichbeganinthe1
2、980'sandhasledtoauni edandautomatedapproachto ndingpartitionbijections.Thesedevelopments,embodiedinthesequence[5,16,8,19,14,20]ofsixpapers,infactformmuchofthecontentofthesenotes,butitseemeddesirabletoprefacethemwithsomegeneralbackgroundonthetheoryofpartitions,andIcouldnotresistendingwiththe
3、developmentin[3],whichconcernsintegerpartitionsinawhollydi erentway.ThelecturenoteswererecordedbyJoeSawada,withsuchcarethatonlyaminimalbungandpolishingwasnecessarytogetthemintothisform.MythanksgotoFrankRuskey,FlorinDiacuandIrinaGavrilovafortheirhospitalityinVictoriaandforfacilitat-ingthisw
4、ork,andtoCarlaSavageforanumberofhelpfulsuggestionsthatimprovedthemanuscript.H.S.W.Philadelphia,PAJuly12,20003Contents0.Overview.................................41.BasicGeneratingFunctions.........................42.IdentitiesandAsymptotics.........................83.PentagonalNumbersandPref
5、abs.....................154.TheInvolutionPrinciple.........................195.Remmel'sbijectionmachine........................206.Sieveequivalence............................247.Gordon'salgorithm...........................268.TheacceleratedalgorithmofKathyO'Hara.................289.Equidis
6、tributedpartitionstatistics.....................2910.Countingtherationalnumbers......................30References...............................3440.OverviewWhatI'dliketodointheselecturesistogive, rst,areviewoftheclassicaltheoryofintegerpartitions,andthentodiscusssomemorerecentdevelopments.
7、Thelatterwillrevolvearoundachainofsixpapers,publishedsince1980,byGarsia-Milne,Je Remmel,BasilGordon,KathyO'Hara,andmyself.Inthesepaperswhatemergesisauni edandautomatedmethodfordealingwithalargeclassofpartitionidentities.ByapartitionidentityIwillmeanatheo
