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.

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