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EnglishA 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
| 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 |
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