A permutomino of size n is a polyomino determined by particular pairs (1, 2) of permutations of n. Here we study various classes of convex permutominoes. We determine some combinatorial properties and, in particular, the characterization for the permutations defining convex, directed-convex, and parallelogram permutominoes. Using standard combinatorial techniques we provide a recursive decomposition for permutations associated with convex permutominoes, and we derive a closed formula for the number of these permutations of size n.
Disanto, F., Frosini, A., Pinzani, R., Rinaldi, S. (2008). THE COMBINATORICS OF CONVEX PERMUTOMINOES. SOUTHEAST ASIAN BULLETIN OF MATHEMATICS, 32, 883-912.
THE COMBINATORICS OF CONVEX PERMUTOMINOES
RINALDI, SIMONE
2008-01-01
Abstract
A permutomino of size n is a polyomino determined by particular pairs (1, 2) of permutations of n. Here we study various classes of convex permutominoes. We determine some combinatorial properties and, in particular, the characterization for the permutations defining convex, directed-convex, and parallelogram permutominoes. Using standard combinatorial techniques we provide a recursive decomposition for permutations associated with convex permutominoes, and we derive a closed formula for the number of these permutations of size n.
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https://hdl.handle.net/11365/10511
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