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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Zbl DOI arXiv
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 
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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     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},
     zbl = {1498.05051},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/11122/}
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