18 citations · 64 across the 25 of their papers we have counts for
37 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.…
A combinatorial characterization of binomial edge ideals
Davide Bolognini, Antonio Macchia, Giancarlo Rinaldo +1
Several algebraic properties of a binomial edge ideal can be interpreted in terms of combinatorial properties of its associated graph . In particular, the so-called cut se…
Cohen-Macaulay binomial edge ideals of small graphs
Davide Bolognini, Antonio Macchia, Giancarlo Rinaldo +1
A combinatorial property that characterizes Cohen-Macaulay binomial edge ideals has long been elusive. A recent conjecture ties the Cohen-Macaulayness of a binomial edge ideal $J_G…
Level and pseudo-Gorenstein binomial edge ideals
Giancarlo Rinaldo, Rajib Sarkar
We prove that level binomial edge ideals with regularity 2 and pseudo-Gorenstein binomial edge ideals with regularity 3 are cones, and we describe them completely. Also, we charact…