Polyominoes determined by permutations: enumeration via bijections

Disanto, F.; Duchi, E.; Pinzani, Renzo; Rinaldi, S.

doi:10.1007/s00026-011-0121-6

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]

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Titolo:	Polyominoes determined by permutations: enumeration via bijections
Autori di Ateneo:	F. Disanto E. Duchi PINZANI, RENZO S. Rinaldi mostra contributor esterni nascondi contributor esterni
Autori:	F. Disanto; E. Duchi; PINZANI, RENZO; S. Rinaldi
Anno di registrazione:	2012
Rivista:	ANNALS OF COMBINATORICS
Volume:	16
Pagina iniziale:	57
Pagina finale:	75
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
Handle:	http://hdl.handle.net/2158/393615
Appare nelle tipologie:	1a - Articolo su rivista

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