Matroids on Eight Elements with the Half-Plane Property and Related Concepts
Abstract.
We classify all matroids with at most eight elements that have the half-plane property, and we provide a list of some matroids on nine elements that have and that do not 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.
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Acknowledgments.
We thank several anonymous referees for providing helpful comments on the paper.
Supplementary Materials
Index of Supplementary Materials
Title of paper: Matroids on Eight Elements with the Half-Plane Property and Related Concepts
Authors: Mario Kummer and Büşra Sert
File: M149064_01.pdf
Type: pdf file
Contents: Additional explanation on the source code for tests and tables to support some results in the main text.
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File: M149064_02.zip
Type: Compressed Code Files
Contents: Macaulay2 code for tests on matroids on 8 elements and for creating symbolic certificates. Sage code for the comparison of minors of matroids and the cataloge of matroids in sage. Julia code for finding and evaluating critical points for matroids on 9 elements.
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Information & Authors
Information
Published In
SIAM Journal on Discrete Mathematics
Pages: 2208 - 2227
DOI: 10.1137/22M1490648
ISSN (online): 1095-7146
Copyright
© 2023 Society for Industrial and Applied Mathematics.
History
Submitted: 19 April 2022
Accepted: 11 May 2023
Published online: 25 September 2023
Keywords
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Funding Information
Deutsche Forschungsgemeinschaft (DFG): 421473641
Funding: Both authors have been supported by the DFG under grant 421473641.
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