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

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.
Rinaldo, G.; Romeo, F.
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]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11572/299577
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