1 citations · 1 across the 3 of their papers we have counts for
9 papers
Terracini matroids: algebraic matroids of secants and embedded joins
Fatemeh Mohammadi, Jessica Sidman, Louis Theran
Applications of algebraic geometry have sparked much recent work on algebraic matroids. An algebraic matroid encodes algebraic dependencies among coordinate functions on a variety.…
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.…
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…
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…