Table of Contents
International Journal of Combinatorics
Volume 2013, Article ID 528584, 6 pages
http://dx.doi.org/10.1155/2013/528584
Research Article

Some Inverse Relations Determined by Catalan Matrices

Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou, Gansu 730050, China

Received 24 June 2013; Revised 21 August 2013; Accepted 21 August 2013

Academic Editor: Laszlo A. Szekely

Copyright © 2013 Sheng-liang Yang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We use the -sequence and -sequence of Riordan array to characterize the inverse relation associated with the Riordan array. We apply this result to prove some combinatorial identities involving Catalan matrices and binomial coefficients. Some matrix identities obtained by Shapiro and Radoux are all special cases of our identity. In addition, a unified form of Catalan matrices is introduced.