Table of Contents
Journal of Discrete Mathematics
Volume 2013 (2013), Article ID 734836, 6 pages
http://dx.doi.org/10.1155/2013/734836
Research Article

Determinant Representations of Polynomial Sequences of Riordan Type

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

Received 12 November 2012; Revised 19 January 2013; Accepted 27 January 2013

Academic Editor: Gi Sang Cheon

Copyright © 2013 Sheng-liang Yang and Sai-nan Zheng. 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

In this paper, using the production matrix of a Riordan array, we obtain a recurrence relation for polynomial sequence associated with the Riordan array, and we also show that the general term for the sequence can be expressed as the characteristic polynomial of the principal submatrix of the production matrix. As applications, a unified determinant expression for the four kinds of Chebyshev polynomials is given.