Boussicault, Adrien and Rinaldi, Simone and Socci, Samanta
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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.