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.
A closed formula for the number of convex permutominoes / F.DISANTO; A. FROSINI; R.PINZANI ; S.RINALDI. - In: ELECTRONIC JOURNAL OF COMBINATORICS. - ISSN 1077-8926. - ELETTRONICO. - 14:(2007), pp. 361-376.
A closed formula for the number of convex permutominoes
FROSINI, ANDREA;PINZANI, RENZO;
2007
Abstract
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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