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 / Rinaldo, G.; Romeo, F.. - In: JOURNAL OF ALGEBRAIC COMBINATORICS. - ISSN 0925-9899. - STAMPA. - 2021:(2021). [10.1007/s10801-021-01017-x]
Hilbert series of simple thin polyominoes
Rinaldo G.;Romeo F.
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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