Strictness of the log-concavity of generating polynomials of matroids

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 independent set are log-concave on the positive orthant. Using these, they obtain some combinatorial inequalities matroids including a solution of strong Mason's conjecture. In this paper, we study strictness log-concavity these polynomials determine when equality holds in inequalities. We also consider generalization our result to morphisms matroids.