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.
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics