Adrien Boussicault ; Simone Rinaldi ; Samanta Socci - The number of directed $k$-convex polyominoes

dmtcs:2465 - Discrete Mathematics & Theoretical Computer Science, January 1, 2015, DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015) - https://doi.org/10.46298/dmtcs.2465
The number of directed $k$-convex polyominoesArticle

Authors: Adrien Boussicault 1; Simone Rinaldi 2; Samanta Socci 2

  • 1 Laboratoire Bordelais de Recherche en Informatique
  • 2 Dipartimento di Ingegneria dell'informazione e scienze matematiche [Siena]

We present a new method to obtain the generating functions for directed convex polyominoes according to several different statistics including: width, height, size of last column/row and number of corners. This method can be used to study different families of directed convex polyominoes: symmetric polyominoes, parallelogram polyominoes. In this paper, we apply our method to determine the generating function for directed $k$-convex polyominoes.We show it is a rational function and we study its asymptotic behavior.

https://doi.org/10.46298/dmtcs.2465
Source: HAL:hal-01337797v1
Volume: DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)
Section: Proceedings
Published on: January 1, 2015
Imported on: November 21, 2016
Keywords: degree of convexity,tree,directed convex polyomino,Parallelogram polyomino,path,generating function.,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
Licence: Attribution 4.0 International (CC BY 4.0)

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