The Generalization And Application Of Riordan Matrix

Along with the rapid development of the computer and our country’s science, Combin-atorial Mathematics, as a kind of science research tools, is used more and more widely. Rior-dan matrix is a kind of important matrix,we can describe combinatorial numbers with two fu-nctions by using Riordan matrix,change the discussing of combinatorial numbers into the dis-cussing of matrix.In this paper, we generalize the concept of Riordan matrices to a kind of matrix sequenceand study the pattern problems of arrangements.The contents can be summarized as follows:In chapter Ⅰ, we introduce the background of Riordan matrix, then give the concept of ge-nerating function and give some generating function of important combinatorial numbers.ChapterⅡ can be divided into four sections: first we give the concept and property of R-iordan matrix,then we define one kind of matrix sequence:[g (x), f (x)], and then give someproperty of the sequence. Finally,we use this kind of matrix sequence to discuss somecombinatorial identities.In chapter Ⅲ, we introduce pattern problems of permutations,it is the basis of theproblems of arrangement patterns.Chapter Ⅳ we use Riordan matrix to study the problems of arrangement patterns.