Zobrazeno 1 - 10
of 20
pro vyhledávání: '"05B50, 05E40"'
Autor:
Navarra, Francesco
In this article we investigate the shellability of the flag simplicial complexes attached to non-simple and thin polyominoes. As a consequence, we obtain the Cohen-Macaulayness and a combinatorial interepetation of the $h$-polynomial of the related c
Externí odkaz:
http://arxiv.org/abs/2408.12367
Let $\mathcal{P}$ be a collection of cells and $I_\mathcal{P}$ be the associated ideal of inner $2$-minors as defined by A. A. Qureshi in 2012. In this paper, we provide a description of the package $\texttt{PolyominoIdeals}$ for the computer algebra
Externí odkaz:
http://arxiv.org/abs/2403.06743
Autor:
Dinu, Rodica, Navarra, Francesco
We investigate the algebraic properties of the coordinate ring of grid polyominoes. This class of non-simple and thin polyominoes was introduced by Mascia, Rinaldo, and Romeo, but not much is known about their polyomino ideals, $I_{\mathcal{P}}$, and
Externí odkaz:
http://arxiv.org/abs/2309.01818
Autor:
Jahangir, Rizwan, Navarra, Francesco
Let $\mathcal{P}$ be a frame polyomino, a new kind of non-simple polyomino. In this paper we study the $h$-polynomial of $K[\mathcal{P}]$ in terms of the switching rook polynomial of $\mathcal{P}$ using the shellable simplicial complex $\Delta(\mathc
Externí odkaz:
http://arxiv.org/abs/2306.11467
In this article, we study the primary decomposition of some binomial ideals. In particular, we introduce the concept of polyocollection, a combinatorial object that generalizes the definitions of collection of cells and polyomino, that can be used to
Externí odkaz:
http://arxiv.org/abs/2302.08337
Autor:
Dinu, Rodica, Navarra, Francesco
We study the K\H{o}nig type property for non-simple polyominoes. We prove that, for closed path polyominoes, the polyomino ideals are of K\H{o}nig type, extending the results of Herzog and Hibi for simple thin polyominoes. As an application of this r
Externí odkaz:
http://arxiv.org/abs/2210.12665
Publikováno v:
Bulletin of the Iranian Mathematical Society, \textbf{49}, 22 (2023)
Let $\mathcal{P}$ 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 $h$-polynomial of $K[\mathcal{P}]$, showing that it is the rook polynomial of $\mathcal{P}$.
Externí odkaz:
http://arxiv.org/abs/2205.08375
Publikováno v:
The Electronic Journal of Combinatorics, 29 (2022)
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 Gr\"obner basis with respect to these monomial ord
Externí odkaz:
http://arxiv.org/abs/2205.08251
In this paper we study the primality of weakly connected collections of cells, showing that the ideal generated by inner 2-minors attached to a weakly connected and simple collection of cells is the toric ideal of the edge ring of a weakly chordal bi
Externí odkaz:
http://arxiv.org/abs/2106.02155
Autor:
Cisto, Carmelo, Navarra, Francesco
In this paper we introduce a new class of polyominoes, called closed paths, and we study the primality of their associated ideal. Inspired by an existing conjecture that characterizes the primality of a polyomino ideal by nonexistence of zig-zag walk
Externí odkaz:
http://arxiv.org/abs/2006.13935