1 citations · 3 across the 8 of their papers we have counts for
8 papers
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…
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…
Decomposing conditional independence ideals with hidden variables
Yulia Alexandr, Kristen Dawson, Hannah Friedman +3
We study a family of determinantal ideals whose decompositions encode the structural zeros in conditional independence models with hidden variables. We provide explicit decompositi…
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…
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…