The Number of Convex Polyominoes with Given Height and Width
Combinatorics
2019-03-05 v1
Abstract
We give a new combinatorial proof for the number of convex polyominoes whose minimum enclosing rectangle has given dimensions. We also count the subclass of these polyominoes that contain the lower left corner of the enclosing rectangle (directed polyominoes). We indicate how to sample random polyominoes in these classes. As a side result, we calculate the first and second moments of the number of common points of two monotone lattice paths between two given points.
Keywords
Cite
@article{arxiv.1903.01095,
title = {The Number of Convex Polyominoes with Given Height and Width},
author = {Kevin Buchin and Man-Kwun Chiu and Stefan Felsner and Günter Rote and André Schulz},
journal= {arXiv preprint arXiv:1903.01095},
year = {2019}
}
Comments
18 pages, 8 figures