F. Romeo

activity

20172026

most citedPrimality of multiply connected polyominoes

10 citations · 20 across the 9 of their papers we have counts for

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math.AC2026

Diagonal F-threshold of binomial edge ideals

Giancarlo Rinaldo, Francesco Romeo

We compute the diagonal $F$ -threshold of binomial edge ideals associated to graphs in the case of cycles, cycles with whiskers, bipartite graphs, and block graphs. Moreover, we pro…

math.AC2024

Sequentially Cohen-Macaulay binomial edge ideals

Ernesto Lax, Giancarlo Rinaldo, Francesco Romeo

We prove that wheels and block graphs have sequentially Cohen-Macaulay binomial edge ideals. Moreover, we provide a construction of new families of sequentially Cohen-Macaulay grap…

math.AC2023

Level and pseudo-Gorenstein path polyominoes

Giancarlo Rinaldo, Francesco Romeo, Rajib Sarkar

We classify path polyominoes which are level and pseudo-Gorenstein. Moreover, we compute all level and pseudo-Gorenstein simple thin polyominoes with rank less than or equal to 10.…

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★ 10 cited

Primality of multiply connected polyominoes

Carla Mascia, Giancarlo Rinaldo, Francesco Romeo

It is known that the polyomino ideal of simple polyominoes is prime. In this paper, we focus on multiply connected polyominoes, namely polyominoes with holes, and observe that the…

math.AC2018★ 3 cited

2-dimensional vertex decomposable circulant graphs

Francesco Romeo, Giancarlo Rinaldo

Let $G$ be the circulant graph $C_{n} (S)$ with $S \subseteq {1, \dots, ⌊ \frac{n}{2} ⌋}$ and let $Δ$ be its independence complex. We describe the well-covered…