F. Romeo

activity

20182022

collaborators

8 papers

math.AC2022

The Stanley-Reisner ideal of the rook complex of polyominoes

Francesco Romeo

We study the properties of the rook complex $R$ of a polyomino $P$ seen as independence complex of a graph $G$ , and the associated Stanley--Reisner ideal $I_\ma…

math.AC2021

$(S_{2})$ -condition and Cohen-Macaulay binomial edge ideals

Alberto Lerda, Carla Mascia, Giancarlo Rinaldo +1

We describe the simplicial complex $Δ$ such that the initial ideal of $J_{G}$ is the Stanley-Reisner ideal of $Δ$ . By $Δ$ we show that if $J_{G}$ is $(S_{2})$ then $G$ is accessible. We…

math.AC2020

Hilbert Series of simple thin polyominoes

Giancarlo Rinaldo, Francesco Romeo

Let P be a simple thin polyomino, roughly speaking a polyomino that has no holes and does not contain a square tetromino as a subpolyomino. In this paper, we determine the reduced…

math.AC2020

Primality of polyomino ideals by quadratic Gröbner basis

Carla Mascia, Giancarlo Rinaldo, Francesco Romeo

In this work, we provide a necessary and sufficient condition on a polyomino ideal for having the set of inner 2-minors as degree reverse lexicographic Gröbner basis, due to combin…

math.AC2019

Regularity and Gorenstein property of the $L$ -convex Polyominoes

Viviana Ene, Jürgen Herzog, Ayesha Asloob Qureshi +1

We study the coordinate ring of an $L$ -convex polyomino, determine its regularity in terms of the maximal number of rooks that can be placed in the polyomino. We also characterize…

math.AC2019

Primality of multiply connected polyominoes