On the combinatorial local log-concavity conjecture and a result of Stanley

TL;DR

This paper clarifies that the combinatorial local log-concavity conjecture by Gross et al. is a consequence of a prior result by Stanley, linking two important combinatorial concepts.

Contribution

It demonstrates that the conjecture is not independent but follows directly from Stanley's earlier theorem, simplifying the understanding of the conjecture's validity.

Findings

The local log-concavity conjecture is implied by Stanley's theorem.

The paper clarifies the relationship between two combinatorial results.

It reduces the conjecture's status to a corollary of existing work.

Abstract

The purpose of this note is to explain that the combinatorial local log-concavity conjecture introduced by Gross, Mansour, Tucker and Wang (Eur. J. Comb. 52, 207-222, 2016) in fact follows from a result of Stanley (Eur. J. Comb. 32 (6), 937-943, 2011).