On the rook polynomial of grid polyominoes
Combinatorics
2026-03-10 v2 Commutative Algebra
Abstract
Grid polyominoes form a class of thin polyominoes with one or more holes arranged in a grid-like pattern in the plane. In this paper, we prove that the rook polynomial of grid polyominoes coincides with the h-polynomial of their corresponding coordinate ring. Our approach is based on the theory of simplicial complexes and extends previous results for frame polyominoes, which are special cases of polyominoes with exactly one hole.
Keywords
Cite
@article{arxiv.2309.01818,
title = {On the rook polynomial of grid polyominoes},
author = {Rodica Dinu and Francesco Navarra},
journal= {arXiv preprint arXiv:2309.01818},
year = {2026}
}
Comments
24 pages, 39 figures. To appear in Discrete Mathematics