English

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 h(t)/(1t)dh(t)/(1-t)^d of K[P] by proving that h(t)h(t) 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}
}
R2 v1 2026-06-23T16:20:29.533Z