A Bijection for Directed-Convex Polyominoes
Del Lungo, Alberto ; Mirolli, Massimo ; Pinzani, Renzo ; Rinaldi, Simone
HAL, hal-01182978 / Harvested from HAL
Text on HAL
In this paper we consider two classes of lattice paths on the plane which use \textitnorth, \textiteast, \textitsouth,and \textitwest unitary steps, beginningand ending at (0,0).We enumerate them according to the number ofsteps by means of bijective arguments; in particular, we apply the cycle lemma.Then, using these results, we provide a bijective proof for the number of directed-convex polyominoes having a fixed number of rows and columns.
Publié le : 2001-07-04
Classification:  cycle lemma,  directed-convex polyominoes,  binomial coefficients,  lattice paths,  [INFO]Computer Science [cs],  [INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG],  [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM],  [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO] 
@article{hal-01182978,
     author = {Del Lungo, Alberto and Mirolli, Massimo and Pinzani, Renzo and Rinaldi, Simone},
     title = {A Bijection for Directed-Convex Polyominoes},
     journal = {HAL},
     volume = {2001},
     number = {0},
     year = {2001},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-01182978}
}

Del Lungo, Alberto; Mirolli, Massimo; Pinzani, Renzo; Rinaldi, Simone. A Bijection for Directed-Convex Polyominoes. HAL, Tome 2001 (2001) no. 0, . http://gdmltest.u-ga.fr/item/hal-01182978/