2005/07/11 by Luca Ferrari, Ferrari, Luca, Renzo Pinzani +1
Mathematics · #05A10 #15A36 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05A10 #msc:15A36
paper · pdf · doi:10.48550/arxiv.math/0507210
Submitted. The paper has been presented at the conference "Paths, Permutations and Trees", held in Tianjin, 2004, February, 25-27
arxiv created 2005/07/11 · arxiv updated 2009/12/01
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.