Catalan-like numbers and succession rules

Details Catalan-like numbers and succession rules Catalan-like numbers and succession rules

2005-07-11

arxiv.org/abs/math/0507210v1

Mathematics

Combinatorics

Submitted. The paper has been presented at the conference "Paths, Permutations and Trees", held in Tianjin, 2004, February, 25

Scientific paper

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.

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