The number of directed k-convex polyominoes
Combinatorics
2015-01-06 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1501.00872,
title = {The number of directed k-convex polyominoes},
author = {Adrien Boussicault and Simone Rinaldi and Samanta Socci},
journal= {arXiv preprint arXiv:1501.00872},
year = {2015}
}