6 citations · 13 across the 7 of their papers we have counts for
21 papers
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…
Powers of monomial ideals with characteristic-dependent Betti numbers
Davide Bolognini, Antonio Macchia, Francesco Strazzanti +1
We explore the dependence of the Betti numbers of monomial ideals on the characteristic of the field. A first observation is that for a fixed prime either the -th Betti numb…
General non-realizability certificates for spheres with linear programming
Joao Gouveia, Antonio Macchia, Amy Wiebe
In this paper we present a simple technique to derive certificates of non-realizability for an abstract polytopal sphere. Our approach uses a variant of the classical algebraic cer…
Cohen-Macaulay binomial edge ideals and accessible graphs
Davide Bolognini, Antonio Macchia, Francesco Strazzanti
The cut sets of a graph are special sets of vertices whose removal disconnects the graph. They are fundamental in the study of binomial edge ideals, since they encode their minimal…
Slack Ideals in Macaulay2
Antonio Macchia, Amy Wiebe
Recently Gouveia, Thomas and the authors introduced the slack realization space, a new model for the realization space of a polytope. It represents each polytope by its slack matri…