Several Conclusions Related To The Riordan Array

Combinatorial identities play an important role in combinatorial mathematics,and they are used in the specific calculations of various disciplines.Research on discovering new combinatorial identities and exploring proof methods is still important and mean-ingful.In many methods for discovering and proving combined identities,the Riordan array method is one of the most effective tools.This paper will discuss the Riordan array from the theoretical extension and method application of Riordan array.Firstly,in theory,the isomorphic mapping is used to generalize the Riordan group to the(r,?)-Riordan group and the general conclusions related to the(r,?)-Riordan group are given.It is pointed out that the essence of Riordan group and(r,?)-Riordan group is the corresponding variation of matrix multiplication under different notation systems.Secondly,in application,based on the work of L.W.Shapiro,H.Gould,R.Sprugnoli,Yin dong-sheng and others,it generalizes Abel identity,important conclusions relat-ed to Abel identity and Gould identity,and thus obtains a series of theorems.By us-ing Riordan array method,a series of new combinatorial identities related to binomial coefficients(?)and(?)are constructed and proved.Representative conclusions are:...