Matroids on Eight Elements with the Half-Plane Property and Related Concepts

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 25 Sep 2023Embargo end date: 01 Nov 2021 English Publisher:Society for Industrial & Applied Mathematics (SIAM)Journal:SIAM Journal on Discrete Mathematics, volume 37, pages 2,208-2,227 (issn: 0895-4801, eissn: 1095-7146,

Copyright policy )Funded by:DFG | unidentified

Authors: Kummer, Mario; Sert, Büşra;

doi: 10.1137/22m1490648 , 10.5281/zenodo.5710290 , 10.5281/zenodo.6109216 , 10.5281/zenodo.5710289 , 10.48550/arxiv.2111.09610

arXiv: 2111.09610

Matroids on Eight Elements with the Half-Plane Property and Related Concepts

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Abstract

Abstract: We classify all matroids with at most 8 elements that have the half-plane property. Furthermore, we prove that several classes of matroids and polynomials that are motivated by the theory of semidefinite programming are closed under taking minors and under passing to faces of the Newton polytope.

Both authors have been supported by the DFG under Grant No.421473641.

Related Organizations

TU Dresden
Germany

Keywords

spectrahedral cones, hyperbolic polynomials, matroid polytopes, Combinatorial aspects of matroids and geometric lattices, 05B35, 90C22, Optimization and Control (math.OC), determinantal representability, FOS: Mathematics, Mathematics - Combinatorics, Semidefinite programming, Rayleigh, Combinatorics (math.CO), half-plane property, spectrahedral representability, Matroids in convex geometry (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.), Mathematics - Optimization and Control, matroids

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