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 satised 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.
Rinaldi, S., Disanto, F., Frosini, A., Pinzani, R. (2007). A closed formula for the number of convex permutominoes. ELECTRONIC JOURNAL OF COMBINATORICS, 14(1).
A closed formula for the number of convex permutominoes
RINALDI, SIMONE;
2007-01-01
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 satised 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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https://hdl.handle.net/11365/37749
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