Hilbert Series of simple thin polyominoes
Commutative Algebra
2020-06-23 v2 Combinatorics
Abstract
Let P be a simple thin polyomino, roughly speaking a polyomino that has no holes and does not contain a square tetromino as a subpolyomino. In this paper, we determine the reduced Hilbert series of K[P] by proving that is the rook polynomial of P. As an application, we characterize the Gorenstein simple thin polyominoes.
Cite
@article{arxiv.2006.08512,
title = {Hilbert Series of simple thin polyominoes},
author = {Giancarlo Rinaldo and Francesco Romeo},
journal= {arXiv preprint arXiv:2006.08512},
year = {2020}
}