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]
Titolo: | Polyominoes determined by permutations: enumeration via bijections | |
Autori di Ateneo: | ||
Autori: | F. Disanto; E. Duchi; PINZANI, RENZO; S. Rinaldi | |
Anno di registrazione: | 2012 | |
Rivista: | ||
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 |