1 citations · 3 across the 12 of their papers we have counts for
13 papers
Combinatorial bounds for the v-number of binomial edge ideals
Emiliano Liwski
We study the local -numbers of binomial edge ideals from a combinatorial perspective. For each minimal prime of , indexed by a cutset …
-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…
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. E…
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 comin…
Decomposing Conditional Independence Ideals with Hidden Variables: A Matroid-Theoretic Approach
Emiliano Liwski
We study a class of determinantal ideals arising from conditional independence (CI) statements with hidden variables. Such CI statements translate into determinantal conditions on…
The V-Number of Binomial Edge Ideals: Minimal Cuts and Cycle Graphs
Emiliano Liwski
The v-number of a graded ideal is an invariant recently introduced in the context of coding theory, particularly in the study of Reed--Muller-type codes. In this work, we study the…
Algebraic Geometry of Cactus, Pascal, and Pappus Matroids
Emiliano Liwski, Fatemeh Mohammadi, Lisa Vandebrouck
We study rank-three matroids, known as point-line configurations, and their associated matroid varieties, defined as the Zariski closures of their realization spaces. Our focus is…
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…
Minimal matroids in dependency posets: algorithms and applications to computing irreducible decompositions of circuit varieties
Emiliano Liwski, Fatemeh Mohammadi
We study point-line configurations, their minimal matroids, and their associated circuit varieties. We present an algorithm for identifying the minimal matroids of these configurat…
Irreducibility, Smoothness, and Connectivity of Realization Spaces of Matroids and Hyperplane Arrangements
Emiliano Liwski, Fatemeh Mohammadi
We study the realization spaces of matroids and hyperplane arrangements. First, we define the notion of naive dimension for the realization space of matroids and compare it with th…
Representations of Yokonuma--Hecke algebras
Emiliano Liwski, Martín Mereb
The Iwahori--Hecke and Yokonuma--Hecke algebras have played crucial roles in algebraic combinatorics and the representation theory of finite groups. In this work, we use classical…
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…
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…