Special Combinatorial Sequences And Probabilistic Method

In this thesis,we mainly study the application of probabilistic method in combinato-rial sequences,and calculate the moment representations of a variety of new combinatorial sequences.Then we derive the different forms of moment representations,and obtain a series of combinatorial identities of the relationships between new combinatorial sequences and classical combinatorial sequences1.We introduce the background of combinatorics,the domestic and overseas re-search status about higher-order generalized Genocchi sequences and several types of the degenerate Daehee numbers and relevant knowledge of probability theory2.We mainly make use of the probabilistic method to calculate the moment repre-sentation of generalized higher-order Genocchi polynomials.Different forms of general-ized higher-order Genocchi polynomials are proved by probability methods.Then new identities of the relationships between generalized higher-order Genocchi sequences and Fibonacci sequences,Bell sequences,Bernoulli sequences,Euler sequences are established3.Using higher-order moments and characteristic functions of the uniform distri-bution and gamma distribution,we calculate the different moment representations of the degenerate Daehee sequences of the third kind,the degenerate Daehee sequences of higher-order and Daehee sequences of the second kind.After studying the relationships between the above sequences and degenerate Stirling sequences of the two kinds and the degenerate Bernoulli sequences,the moment representations of them are obtained.