Strictness of the log-concavity of generating polynomials of matroids

Satoshi Murai, Takahiro Nagaoka*, Akiko Yazawa

*この研究の対応する著者

研究成果: Article査読

1 被引用数 (Scopus)

抄録

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.

本文言語English
論文番号105351
ジャーナルJournal of Combinatorial Theory. Series A
181
DOI
出版ステータスPublished - 2021 7

ASJC Scopus subject areas

  • 理論的コンピュータサイエンス
  • 離散数学と組合せ数学
  • 計算理論と計算数学

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