Geodesic
On Gröbner basis and Cohen-Macaulay property of closed path polyominoes
Carmelo Cisto1 ; Francesco Navarra2 ; Rosanna Utano2
1University of Messina
2Universitá di Messina
The electronic journal of combinatorics, Tome 29 (2022) no. 3
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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.
DOI : 10.37236/11122
Classification : 05B50, 05E40, 13P10, 13C05, 13G05, 13C14
Mots-clés : monomial orders, polyomino ideal, zig-zag walks

Carmelo Cisto  1   ; Francesco Navarra  2   ; Rosanna Utano  2

1 University of Messina
2 Universitá di Messina 
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     author = {Carmelo Cisto and Francesco Navarra and Rosanna Utano},
     title = {On {Gr\"obner} basis and {Cohen-Macaulay} property of closed path polyominoes},
     journal = {The electronic journal of combinatorics},
     year = {2022},
     volume = {29},
     number = {3},
     doi = {10.37236/11122},
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     url = {http://geodesic.mathdoc.fr/articles/10.37236/11122/}
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Carmelo Cisto; Francesco Navarra; Rosanna Utano. On Gröbner basis and Cohen-Macaulay property of closed path polyominoes. The electronic journal of combinatorics, Tome 29 (2022) no. 3. doi: 10.37236/11122

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