On the enumeration of column-convex permutominoes

Abstract : We study the enumeration of \emphcolumn-convex permutominoes, i.e. column-convex polyominoes defined by a pair of permutations. We provide a direct recursive construction for the column-convex permutominoes of a given size, based on the application of the ECO method and generating trees, which leads to a functional equation. Then we obtain some upper and lower bounds for the number of column-convex permutominoes, and conjecture its asymptotic behavior using numerical analysis.
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Nicholas R. Beaton, Filippo Disanto, Anthony J. Guttmann, Simone Rinaldi. On the enumeration of column-convex permutominoes. 23rd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2011), 2011, Reykjavik, Iceland. pp.111-122. ⟨hal-01215087⟩

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