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1、ADVANCEDDETERMINANTCALCULUSC.KRATTENTHALERyInstitutf?urMathematikderUniversit?atWien,Strudlhofgasse4,A-1090Wien,Austria.E-mail:kratt@pap.univie.ac.atWWW:http://radon.mat.univie.ac.at/People/krattDedicatedtothepioneerofdeterminantevaluations(amongmanyotherthings),GeorgeAndrews
2、Abstract.Thepurposeofthisarticleisthreefold.First,itprovidesthereaderwithafewusefulandecienttoolswhichshouldenableher/himtoevaluatenontrivialde-terminantsforthecasesuchadeterminantshouldappearinher/hisresearch.Second,itlistsanumberofsuchdeterminantsthathavebeenalreadyevaluat
3、ed,togetherwithexplanationswhichtellinwhichcontextstheyhaveappeared.Third,itpointsoutreferenceswherefurthersuchdeterminantevaluationscanbefound.1.IntroductionImagine,youareworkingonaproblem.Asthingsdevelopitturnsoutthat,inordertosolveyourproblem,youneedtoevaluateacertaindeter
4、minant.Maybeyourdeterminantis1det;(1.1)1i;j;ni+jmath.CO/9902004v331May1999ora+bdet;(1.2)1i;jna
