Journal
ADVANCES IN MATHEMATICS
Volume 436, Issue -, Pages -Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.aim.2023.109404
Keywords
Linear extensions; Stanley's inequalities; Contents
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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.
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.
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