## Boussicault, Adrien and Rinaldi, Simone and Socci, Samanta - 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)
The number of directed $k$-convex polyominoes

Authors: Boussicault, Adrien and Rinaldi, Simone and Socci, Samanta

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.

Source : oai: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
Submitted 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]