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Polyominoes determined by permutations

Abstract : In this paper we consider the class of $\textit{permutominoes}$, i.e. a special class of polyominoes which are determined by a pair of permutations having the same size. We give a characterization of the permutations associated with convex permutominoes, and then we enumerate various classes of convex permutominoes, including parallelogram, directed-convex, and stack ones.
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I. Fanti, A. Frosini, E. Grazzini, R. Pinzani, S. Rinaldi. Polyominoes determined by permutations. Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities, 2006, Nancy, France. pp.381-390. ⟨hal-01184680⟩

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