Year: 2026
Type: article
Abstract: . As a direct application of Dilworth truncations of polymatroids, we give short proofs of two theorems: Bernstein’s characterization of algebraic matroids coming from the Hadamard product of two linear spaces, and a formula for the dimension of the amoeba of a complex linear space by Draisma, Eggleston, Pendavingh, Rau, and Yuen. We disprove Bernstein’s conjecture on a characterization of the algebraic matroids of Hadamard products of more than two linear spaces, by giving explicit counterexamples.
DOI: 10.1137/25m1809045
Authors: Dario Antolini, Sean Dewar, Shin-ichi Tanigawa
Institutions: University of Trento, KU Leuven, The University of Tokyo
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funders: National Science Foundation, Istituto Nazionale di Alta Matematica "Francesco Severi", Fonds Wetenschappelijk Onderzoek, KU Leuven, Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni, Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni, Japan Society for the Promotion of Science
Awards: Exploiting combinatorial structures for algebraic and geometric decompositions, Institute for Computational and Experimental Research in Mathematics, Theory and Algorithms for the Identifiable Problem of Point Configurations, 非正曲率空間上の次世代凸最適化, G4869584417, Matroids in Applied and Combinatorial Commutative Algebra
OpenAlex ID: W6929407367