Work

Decomposing Determinantal Varieties from Statistics via Matroid Theory

Year: 2026

Type: preprint

Abstract: We study determinantal varieties from conditional independence models with hidden variables, focusing on their irreducible decompositions, dimensions, degrees, and Gröbner bases. Each variety encodes a collection of matroids, whose flats capture algebraic dependencies among variables. Using this approach, we provide a systematic description of the components, their dimensions, and defining equations, and introduce a combinatorial framework for computing the degree of the determinantal variety. Our approach highlights the central role of matroidal structures in the study of determinantal varieties and extends beyond the reach of current computational techniques.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2601.15128

Authors: Alexandersson, Per, Alexandr, Yulia, Liwski, Emiliano, Mohammadi, Fatemeh, Semnani, Pardis

Topic: Polynomial and algebraic computation

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: Fonds Wetenschappelijk Onderzoek, KU Leuven, Stockholms Universitet

Awards: Exploiting combinatorial structures for algebraic and geometric decompositions, G4869584417, Matroids in Applied and Combinatorial Commutative Algebra, Properties of Matroids: Algebraic and Geometric Perspectives

OpenAlex ID: W7125424248

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