Séminaire Lotharingien de Combinatoire, 86B.9 (2022), 12 pp.
Swee Hong Chan and Igor Pak
Log-Concave Poset Inequalities: Extended Abstract
Abstract.
We study combinatorial inequalities for various classes of set systems:
matroids, morphisms of matroids, polymatroids, and poset antimatroids.
We prove log-concave inequalities for counting certain weighted
feasible words, which generalize and extend several previous results
establishing Mason conjectures for the numbers of independent sets
of matroids.
Additionally, we rederive Stanley's
inequality on the number of certain linear extensions, which we then also extend to the weighted case.
Notably, we also prove matching equality
conditions for all these inequalities.
Received: November 25, 2021.
Accepted: March 4, 2022.
Final version: April 1, 2022.
The following versions are available: