English

On One-Parameter Catalan Arrays

Combinatorics 2015-05-22 v1

Abstract

We present a parametric family of Riordan arrays which are obtained by multiplying any Riordan array with a generalized Pascal array. In particular, we focus on some interesting properties of one-parameter Catalan triangles. We obtain several combinatorial identities that involve two special Catalan matrices, the Chebyshev polynomials of the second kind, some periodic sequences, and the Fibonacci numbers.

Keywords

Cite

@article{arxiv.1505.05568,
  title  = {On One-Parameter Catalan Arrays},
  author = {José Agapito and Ângela Mestre and Pasquale Petrullo and Maria M. Torres},
  journal= {arXiv preprint arXiv:1505.05568},
  year   = {2015}
}

Comments

13 pages

R2 v1 2026-06-22T09:38:25.455Z