10 papers
-number of Lovász-Saks-Schrijver Ideals and (parity) binomial edge ideals of graphs
Manohar Kumar, Emiliano Liwski
In this paper, we introduce a new framework for computing certain localized -numbers of a class of ideals called coordinate-saturated ideals, which includes certain cla…
Paving Matroids: Defining Equations and Associated Varieties
Emiliano Liwski, Fatemeh Mohammadi
We study paving matroids, their realization spaces, and their closures, along with matroid varieties and circuit varieties. Within this context, we introduce three distinct methods…
Decomposing Determinantal Varieties from Statistics via Matroid Theory
Per Alexandersson, Yulia Alexandr, Emiliano Liwski +2
We study determinantal varieties from conditional independence models with hidden variables, focusing on their irreducible decompositions, dimensions, degrees, and Gröbner bases.…
Lovász--Saks--Schrijver Ideals and the Irreducible Components of the Variety of Orthogonal Representations of a Graph
Emiliano Liwski
Given a finite simple graph and a positive integer , one can associate to the Lovász--Saks--Schrijver ideal , an ideal generated by quadratic polynomials comi…
Efficient Algorithms for Maximal Matroid Degenerations and Irreducible Decompositions of Circuit Varieties
Emiliano Liwski, Fatemeh Mohammadi, Rémi Prébet
Matroid theory provides a unifying framework for studying dependence across combinatorics, geometry, and applications ranging from rigidity to statistics. In this work, we study ci…
Solvable and Nilpotent Matroids: Realizability and Irreducible Decomposition of Their Associated Varieties
Emiliano Liwski, Fatemeh Mohammadi
We introduce the families of solvable and nilpotent matroids, examining their realization spaces, closures, and associated matroid and circuit varieties. We study their realizabili…