Ballot matrix as Catalan matrix power and related identities

5Citations
Citations of this article
6Readers
Mendeley users who have this article in their library.

Abstract

We use an analytical approach to find the kth power of the Catalan matrix. Precisely, it is proven that the power of the Catalan matrix is a lower triangular Toeplitz matrix which contains the well-known ballot numbers. A result from [H. S. Wilf, Generatingfunctionology, Academic Press, New York, 1990, Free download available from http://www.math.upenn.edu/wilf/Downld.html.], related to the generating function for Catalan numbers, is extended to the negative integers. Three interesting representations for Catalan numbers by means of the binomial coefficients and the hypergeometric functions are obtained using relations between Catalan matrix powers. © 2011 Elsevier B.V. All rights reserved.

Cite

CITATION STYLE

APA

Stanimirović, S., Stanimirovi, P., & Ilić, A. (2012). Ballot matrix as Catalan matrix power and related identities. Discrete Applied Mathematics, 160(3), 344–351. https://doi.org/10.1016/j.dam.2011.10.016

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free