Alberto Del Lungo ; Massimo Mirolli ; Renzo Pinzani ; Simone Rinaldi - A Bijection for Directed-Convex Polyominoes

dmtcs:2298 - Discrete Mathematics & Theoretical Computer Science, January 1, 2001, DMTCS Proceedings vol. AA, Discrete Models: Combinatorics, Computation, and Geometry (DM-CCG 2001) - https://doi.org/10.46298/dmtcs.2298
A Bijection for Directed-Convex PolyominoesArticle

Authors: Alberto Del Lungo ; Massimo Mirolli 1; Renzo Pinzani 2; Simone Rinaldi 2

  • 1 Department of Mathematics and Computer Science / Dipartimento di Scienze Matematiche e Informatiche "Roberto Magari"
  • 2 Dipartimento di Sistemi e Informatica

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.

https://doi.org/10.46298/dmtcs.2298
Source: HAL:hal-01182978v1
Volume: DMTCS Proceedings vol. AA, Discrete Models: Combinatorics, Computation, and Geometry (DM-CCG 2001)
Section: Proceedings
Published on: January 1, 2001
Imported on: November 21, 2016
Keywords: 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]

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