Strictness of the log-concavity of generating polynomials of matroids

Satoshi Murai, Takahiro Nagaoka, Akiko Yazawa

Research output: Contribution to journalArticlepeer-review

Abstract

Recently, it was proved by Anari–Oveis Gharan–Vinzant, Anari–Liu–Oveis Gharan–Vinzant and Brändén–Huh that, for any matroid M, its basis generating polynomial and its independent set generating polynomial are log-concave on the positive orthant. Using these, they obtain some combinatorial inequalities on matroids including a solution of strong Mason's conjecture. In this paper, we study the strictness of the log-concavity of these polynomials and determine when equality holds in these combinatorial inequalities. We also consider a generalization of our result to morphisms of matroids.

Original languageEnglish
Article number105351
JournalJournal of Combinatorial Theory. Series A
Volume181
DOIs
Publication statusPublished - 2021 Jul

Keywords

  • Hodge–Riemann relation
  • Independent set
  • Lorentzian polynomial
  • Mason's conjecture
  • Matroid
  • Morphism of matroids

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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