Let P be a simple thin polyomino, namely a polyomino that has no holes and does not contain a square tetromino as a subpolyomino. In this paper, we determine the reduced Hilbert–Poincaré 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.
Hilbert series of simple thin polyominoes
Romeo, Francesco
2021-01-01
Abstract
Let P be a simple thin polyomino, namely a polyomino that has no holes and does not contain a square tetromino as a subpolyomino. In this paper, we determine the reduced Hilbert–Poincaré 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.File in questo prodotto:
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