A permutominide is a set of cells in the plane satisfying special connectivity constraints and uniquely defined by a pair of permutations. It naturally generalizes the concept of permutomino, recently investigated by several authors and from different points of view [1, 2, 4, 6, 7]. In this paper, using bijective methods, we determine the enumeration of various classes of convex permutominides, including, parallelogram, directed convex, convex, and row convex permutominides. As a corollary we have a bijective proof for the number of convex permutominoes, which was still an open problem

Polyominoes determined by permutations: enumeration via bijections / F. Disanto; E. Duchi; R. Pinzani; S. Rinaldi. - In: ANNALS OF COMBINATORICS. - ISSN 0218-0006. - STAMPA. - 16:(2012), pp. 57-75. [10.1007/s00026-011-0121-6]

Polyominoes determined by permutations: enumeration via bijections

PINZANI, RENZO;
2012

Abstract

A permutominide is a set of cells in the plane satisfying special connectivity constraints and uniquely defined by a pair of permutations. It naturally generalizes the concept of permutomino, recently investigated by several authors and from different points of view [1, 2, 4, 6, 7]. In this paper, using bijective methods, we determine the enumeration of various classes of convex permutominides, including, parallelogram, directed convex, convex, and row convex permutominides. As a corollary we have a bijective proof for the number of convex permutominoes, which was still an open problem
16
57
75
F. Disanto; E. Duchi; R. Pinzani; S. Rinaldi
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2158/393615
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