6 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…