Luca Ferrari, Renzo Pinzani
Published 2005-07-11Version 1
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.
Comments: Submitted. The paper has been presented at the conference "Paths, Permutations and Trees", held in Tianjin, 2004, February, 25-27
Paley-like graphs over finite fields from vector spaces
Results on the intersection graphs of subspaces of a vector space
Graphs, defined by Weyl distance or incidence, that determine a vector space
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