The extremals of Stanley's inequalities for partially ordered sets

Stanley's inequalities for partially ordered sets establish important log-concavity relations for sequences of linear extensions counts. Their extremals however, i.e., the equality cases of these inequalities, were until now poorly understood with even conjectures lacking. In this work, we solve this problem by providing a complete characterization of the extremals of Stanley's inequalities. Our proof is based on building a new dictionary between the combinatorics of partially ordered sets and the geometry of convex polytopes, which captures their extremal structures. (c) 2023 Elsevier Inc. All rights reserved.

Automated summary

This study provides a new approach to understanding the extremal cases of Stanley's inequalities by establishing a connection between the combinatorics of partially ordered sets and the geometry of convex polytopes.