Catalan-like numbers and succession rules
Abstract
The ECO method and the theory of Catalan-like numbers introduced by Aigner seems two completely unrelated combinatorial settings. In this work we try to establish a bridge between them, aiming at starting a (hopefully) fruitful study on their interactions. We show that, in a linear algebra context (more precisely, using infinite matrices), a succession rule can be translated into a (generalized) Aigner matrix by means of a suitable change of basis in the vector space of one-variable polynomials. We provide some examples to illustrate this fact and apply it to the study of two particular classes of succession rules.
Cite
@article{arxiv.math/0507210,
title = {Catalan-like numbers and succession rules},
author = {Luca Ferrari and Renzo Pinzani},
journal= {arXiv preprint arXiv:math/0507210},
year = {2007}
}
Comments
Submitted. The paper has been presented at the conference "Paths, Permutations and Trees", held in Tianjin, 2004, February, 25-27