10 citations · 20 across the 9 of their papers we have counts for
14 papers
Diagonal F-threshold of binomial edge ideals
Giancarlo Rinaldo, Francesco Romeo
We compute the diagonal -threshold of binomial edge ideals associated to graphs in the case of cycles, cycles with whiskers, bipartite graphs, and block graphs. Moreover, we pro…
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…
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.…
The Stanley-Reisner ideal of the rook complex of polyominoes
Francesco Romeo
We study the properties of the rook complex of a polyomino seen as independence complex of a graph , and the associated Stanley--Reisner ideal $I_\ma…
Squashed entanglement in one-dimensional quantum matter
Alfonso Maiellaro, Francesco Romeo, Roberta Citro +1
Squashed entanglement and its universal upper bound, the quantum conditional mutual information, are faithful measures of bipartite quantum correlations defined in terms of multipa…
Hilbert series of Parallelogram Polyominoes
Ayesha Asloob Qureshi, Giancarlo Rinaldo, Francesco Romeo
We present a conjecture about the reduced Hilbert series of the coordinate ring of a simple polyomino in terms of particular arrangements of non-attacking rooks that can be placed…
-condition and Cohen-Macaulay binomial edge ideals
Alberto Lerda, Carla Mascia, Giancarlo Rinaldo +1
We describe the simplicial complex such that the initial ideal of is the Stanley-Reisner ideal of . By we show that if is then is accessible. We…
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…
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…
Regularity and Gorenstein property of the -convex Polyominoes
Viviana Ene, Jürgen Herzog, Ayesha Asloob Qureshi +1
We study the coordinate ring of an -convex polyomino, determine its regularity in terms of the maximal number of rooks that can be placed in the polyomino. We also characterize…
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…
Chordal circulant graphs and induced matching number
Francesco Romeo
Let be a circulant graph on vertices. In this paper we characterize chordal circulant graphs and then we compute , the induced matching number of . These…
2-dimensional vertex decomposable circulant graphs
Francesco Romeo, Giancarlo Rinaldo
Let be the circulant graph with and let be its independence complex. We describe the well-covered…
On the reduced Euler characteristic of independence complexes of circulant graphs
Giancarlo Rinaldo, Francesco Romeo
Let be the circulant graph with . We study the reduced Euler characteristic of the independen…