13 citations · 50 across the 13 of their papers we have counts for
14 papers
Generalized Numerical semigroups up to isomorphism
Carmelo Cisto, Gioia Failla, Francesco Navarra
A generalized numerical semigroup is a submonoid of with finite complement in it. We characterize isomorphisms between these monoids in terms of permutation of c…
Shellable flag simplicial complexes of non-simple polyominoes
Francesco Navarra
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…
On squarefree powers of simplicial trees
Elshani Kamberi, Francesco Navarra, Ayesha Asloob Qureshi
In this article, we study the squarefree powers of facet ideals associated with simplicial trees. Specifically, we examine the linearity of their minimal free resolution and their…
Collections of cells, binomial ideals and combinatorics
Carmelo Cisto, Rizwan Jahangir, Francesco Navarra
In this paper we provide a description of the package \textit{PolyominoIdeals} for \textit{Macaulay2} that allows to deal with collections of cells, polyominoes and related binomia…
On Cohen-Macaulay non-prime collections of cells
Carmelo Cisto, Rizwan Jahangir, Francesco Navarra
In this paper we investigate Cohen-Macaulayness, Gorensteinness and the Hilbert-Poincaré series for some classes of non-prime collections of cells. In particular, we show that all…
On the rook polynomial of grid polyominoes
Rodica Dinu, Francesco Navarra
Grid polyominoes form a class of thin polyominoes with one or more holes arranged in a grid-like pattern in the plane. In this paper, we prove that the rook polynomial of grid poly…
Shellable simplicial complex and switching rook polynomial of frame polyominoes
Rizwan Jahangir, Francesco Navarra
Let be a frame polyomino, a new kind of non-simple polyomino. In this paper we study the -polynomial of in terms of the switching rook polynomial…
Polyocollection ideals and primary decomposition of polyomino ideals
Carmelo Cisto, Francesco Navarra, Dharm Veer
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…
On some classes of generalized numerical semigroups
Carmelo Cisto, Francesco Navarra
A generalized numerical semigroup is a submonoid of with finite complement in it. In this work we study some properties of three different classes of generalized num…
Non-simple polyominoes of Kőnig type and their canonical module
Rodica Dinu, Francesco Navarra
We study the Kőnig type property for non-simple polyominoes. We prove that, for closed path polyominoes, the polyomino ideals are of Kőnig type, extending the results of Herzog and…
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…
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…
Primality of weakly connected collections of cells and weakly closed path polyominoes
Carmelo Cisto, Francesco Navarra, Rosanna Utano
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 collecti…
Primality of closed path polyominoes
Carmelo Cisto, Francesco Navarra
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 characteri…