We study the enumeration of column-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.
Beaton, N., Disanto, F., Guttmann, T., Rinaldi, S. (2011). On the enumeration of column-convex permutominoes. DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE, 2011, 111-122.
On the enumeration of column-convex permutominoes
Rinaldi S.
2011-01-01
Abstract
We study the enumeration of column-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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https://hdl.handle.net/11365/36159
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