Geodesic
A Bijection for Directed-Convex Polyominoes
Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AA, Discrete Models: Combinatorics, Computation, and Geometry (DM-CCG 2001), DMTCS Proceedings vol. AA, Discrete Models: Combinatorics, Computation, and Geometry (DM-CCG 2001) (2001) Cet article a éte moissonné depuis la source Episciences

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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. 
@article{DMTCS_2001_special_246_a21,
     author = {Del Lungo, Alberto and Mirolli, Massimo and Pinzani, Renzo and Rinaldi, Simone},
     title = {A {Bijection} for {Directed-Convex} {Polyominoes}},
     journal = {Discrete mathematics & theoretical computer science},
     year = {2001},
     volume = {DMTCS Proceedings vol. AA, Discrete Models: Combinatorics, Computation, and Geometry (DM-CCG 2001)},
     doi = {10.46298/dmtcs.2298},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.2298/}
}
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Del Lungo, Alberto; Mirolli, Massimo; Pinzani, Renzo; Rinaldi, Simone. A Bijection for Directed-Convex Polyominoes. Discrete mathematics & theoretical computer science, DMTCS Proceedings vol. AA, Discrete Models: Combinatorics, Computation, and Geometry (DM-CCG 2001), DMTCS Proceedings vol. AA, Discrete Models: Combinatorics, Computation, and Geometry (DM-CCG 2001) (2001). doi: 10.46298/dmtcs.2298

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