71 research outputs found
Catalan-like numbers and succession rules
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.Comment: Submitted. The paper has been presented at the conference "Paths,
Permutations and Trees", held in Tianjin, 2004, February, 25-2
A closed formula for the number of convex permutominoes
In this paper we determine a closed formula for the number of convex
permutominoes of size n. We reach this goal by providing a recursive generation
of all convex permutominoes of size n+1 from the objects of size n, according
to the ECO method, and then translating this construction into a system of
functional equations satisfied by the generating function of convex
permutominoes. As a consequence we easily obtain also the enumeration of some
classes of convex polyominoes, including stack and directed convex
permutominoes
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