Asymptotic Enumeration Methods Of Combinatorics

There are many methods to study combinatorial enumeration.Problems of combinatorial enumeration,and asymptotic enumeration method is one of the most important approach. In this thesis,we investigate problems of combinatorial enumeration by applying asymptotic enumeration method.The main results of this thesis can be summarize as follows:In Chapter 2,we discuss the asymptotic expansions of certain sums by using Laplace's method,we give the asymptotic values of certain sums involving generalized harmonic numbers and binomial coefficients.In Chapter 3,we investigate the properties of some special numbers by Darboux's method. For example,we discuss the asymptotic estimation of Sali(?) numbers and P-Stirling numbers.In Chapter 4,we first establish some numbers identities related to two kinds of generalized harmonic by the method of coefficients.Further more,we compute the asymptotic expansion of sums involving generalized harmonic number by singularity analysis method.