Hilbert Series of simple thin polyominoes

2020/06/15 by Rinaldo, Giancarlo, Romeo, Francesco · 2 citations
#05B50 #13D40 #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2006.08512

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)/(1-t)^d of K[P] by proving that h(t) is the rook polynomial of P. As an application, we characterize the Gorenstein simple thin polyominoes.

Cited by

• Switching rook polynomial of collections of cells
• Switching Rook Polynomials of Collections of Cells: Palindromicity and Domino-Stability

Related

• The h-polynomial and the rook polynomial of some polyominoes
• Hilbert series of Parallelogram Polyominoes
• The Charney-Davis conjecture for simple thin polyominoes
• On the rook polynomial of grid polyominoes
• Thin polytopes: Lattice polytopes with vanishing local h^*-polynomial