組合學(xué)中的漸近計數(shù)方法.pdf

1、大連理工大學(xué)碩士學(xué)位論文組合學(xué)中的漸近計數(shù)方法姓名：封從嬌申請學(xué)位級別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：趙鳳珍20090601組合學(xué)中的漸近計數(shù)方法AsymptoticEnumerationMethodsofCombinatoricsAbstractThereaxemanymethodstostudycombinatorialenumerationProblemsofcombinatorialenumeration，andasymptoti

2、cenumerationmethodisoIleofthemostimportantapproachInthisthesis，weinvestigateproblemsofcombinatorialenumerationbyapplyingasymptoticenumerationmethodThemainresultsofthisthesiscanbesummarizeasfollows：InChapter2wediscussthea

3、symptoticexpansionsofcertainsumsbyuslngLaplace7SmethodwegivetheasymptoticvaluesofcertainsumsinvolvinggeneralizedharmonicnumbersandbinomialcoefficientsInChapter3，weinvestigatethepropertiesofsomespecialnumbersbyDarboux’Sme

4、thodForexample，wediscusstheasymptoticestimationofSali6numbersandP—StirlingnumbersInChapter4，wefirstestablishsomenumbersidentitiesrelatedtotwokindsofgeneralizedharmonicbythemethodofcoemcientsFurthermorewecomputetheasympto

5、ticexpansionofsumsinvolvinggeneralizedharmonicnumberbysingularityanalysismethodKeywords：Stirlingnumbers；harmonicnumbers；Cauchynumbers；generatingfunction；Laplace’Smethod；Darboux’Smethod；singularityanalysismethod；asymptoti