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  1. Home > Articles & Issues >
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  3. A Bijection for Dire ...
Conference paper

A Bijection for Directed-Convex Polyominoes

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
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November 21, 2016
Published on
December 31, 2000
Last modified on
March 31, 2025
Volume 0
DMTCS Proceedings vol. AA, Discrete Models: Combinatorics, Computation, and Geometry (DM-CCG 2001)
Proceedings
DOI
10.46298/dmtcs.2298
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A Bijection for Directed-Convex Polyominoes

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
Abstract
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.
Keywords
  • [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]
  • cycle lemma
  • directed-convex polyominoes
  • binomial coefficients
  • lattice paths
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