| Riordan matrix is one of the main research objects in combinatorial mathemat-ics. It is a kind of special infinite lower triangular matrix. The matrix is extended to the isosceles triangle matrix to the left. We call this matrix as ISO-type trian-gular matrix. The middle column of the ISO-type triangular matrix is the central coefficient of the Riordan matrix. With its middle column as the initial column,the right part of the matrix is the central coefficient matrix of the Riordan matrix.On this basis, we define the (m, r)-central coefficient and (m, r)-central coefficient matrix of Riordan matrix by repeating the above process. As an application, we get some identities from two special Riordan matrices which are Pascal matrix and Catalan matrix.In the first chapter, we introduce the research background of this subject and present the Riordan matrix and Catalan matrix theory.In the second chapter, the concept and research results of central coefficient and r-central coefficient of Riordan matrix are given. Then we give the concept of(m, r)-central coefficient and its generating function.In the third chapter, the half -Riordan matrix and r-central coefficient Riordan matrix are introduced, and then define the (m, r)-central coefficient matrix of the Riordan matrix, and get a lot of very meaningful results. Finally, we study the(m, r)-central coefficient matrix of Pascal matrix and Catalan matrix, and obtain some identities. |
