Séminaire Lotharingien de Combinatoire, 93B.88 (2025), 12 pp.
Jinting Liang and Bruce E. Sagan
Log-Concavity and Log-Convexity via Distributive Lattices
Abstract.
We prove a result on order ideals in distributive lattices, called the Order Ideal Lemma. We indicate how the Order Ideal Lemma implies log-concavity and log-convexity of various sequences involving lattice paths, intervals in Young's lattice, order polynomials, specializations of Schur and Schur Q-functions, Lucas sequences, descent and peak polynomials of permutations, pattern avoidance, set partitions, and noncrossing partitions.
Received: November 15, 2024.
Accepted: February 15, 2025.
Final version: April 1, 2025.
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