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Gamma vectors of partitioned permutohedra

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arxiv 2405.09242 v2 pith:P3WHYL5K submitted 2024-05-15 math.CO math.AGmath.RT

Tatsuya Horiguchi , Mikiya Masuda , Takashi Sato , John Shareshian , Jongbaek Song This is my paper · ORCID
classification math.COmath.AGmath.RT
keywords resultathanasiadisgammapartitionedpermutohedravectorscloselycohomology
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abstract

We determine that $\gamma$-vectors of partitioned permutohedra, thereby generalizing a result of Foata and Sch\"utzenberger. Our result is closely related to a result of Athanasiadis on the representation of the symmetric group on the cohomology of the permutohedral variety. We explain how to derive Athanasiadis' result from ours and vice versa.

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Cited by 1 Pith paper

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  1. Order polytopes of graded posets are gamma-effective

    math.CO 2025-05 conditional novelty 7.0 of 10

    Order polytopes of graded posets are gamma-effective, meaning the equivariant gamma-polynomial of any graded poset has nonnegative integer character coefficients.

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