1 citations · 3 across the 12 of their papers we have counts for
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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…
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…
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…