A closed formula for the number of convex permutominoes

Details A closed formula for the number of convex permutominoes A closed formula for the number of convex permutominoes

2007-02-19

arxiv.org/abs/math/0702550v1

El. J. Combinatorics 14 (2007) #R57

Mathematics

Combinatorics

Scientific paper

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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