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Catalan-like numbers and succession rules

Luca Ferrari·Renzo Pinzani
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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.

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Luca Ferrari, Renzo Pinzani. 2005-07-11. Catalan-like numbers and succession rules. https://arxiv.org/abs/math/0507210

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