In this paper we introduce some monomial orders for the class of closed path polyominoes and we prove that the set of the generators of the polyomino ideal attached to a closed path forms the reduced Gröbner basis with respect to these monomial orders. It is known that the polyomino ideal attached to a closed path containing an L-configuration or a ladder of at least three steps, equivalently having no zig-zag walks, is prime. As a consequence, we obtain that the coordinate ring of a closed path having no zig-zag walks is a normal Cohen-Macaulay domain.

On Gröbner basis and Cohen-Macaulay property of closed path polyominoes

Cisto C.
Primo
Membro del Collaboration Group
;
Navarra F.
Secondo
Membro del Collaboration Group
;
Utano R.
Ultimo
Membro del Collaboration Group
2022-01-01

Abstract

In this paper we introduce some monomial orders for the class of closed path polyominoes and we prove that the set of the generators of the polyomino ideal attached to a closed path forms the reduced Gröbner basis with respect to these monomial orders. It is known that the polyomino ideal attached to a closed path containing an L-configuration or a ladder of at least three steps, equivalently having no zig-zag walks, is prime. As a consequence, we obtain that the coordinate ring of a closed path having no zig-zag walks is a normal Cohen-Macaulay domain.
2022
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11570/3239532
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