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math.AC2022★ 6 cited
On Gröbner bases and Cohen-Macaulay property of closed path polyominoes
Carmelo Cisto, Francesco Navarra, Rosanna Utano
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 pat…
math.AC2022★ 8 cited
Hilbert-Poincaré series and Gorenstein property for some non-simple polyominoes
Carmelo Cisto, Francesco Navarra, Rosanna Utano
Let be a closed path having no zig-zag walks, a kind of non-simple thin polyomino. In this paper we give a combinatorial interpretation of the -polynomial of $K[\m…