The extremals of Stanley’s inequalities for partially ordered sets.(English)Zbl 07781638
Summary: 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.
MSC:
| 06A07 | Combinatorics of partially ordered sets |
| 52B05 | Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.) |
| 05A20 | Combinatorial inequalities |
Cite
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