Gamma vectors of partitioned permutohedra

Tatsuya Horiguchi; Mikiya Masuda; Takashi Sato; John Shareshian; Jongbaek Song

Gamma vectors of partitioned permutohedra

Combinatorics 2025-05-01 v2 Algebraic Geometry Representation Theory

Authors: Tatsuya Horiguchi , Mikiya Masuda , Takashi Sato , John Shareshian , Jongbaek Song

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.

Keywords

gamma vectors partitioned permutohedra Foata-Schützenberger theorem symmetric group cohomology permutohedral variety

Cite

@article{arxiv.2405.09242,
  title  = {Gamma vectors of partitioned permutohedra},
  author = {Tatsuya Horiguchi and Mikiya Masuda and Takashi Sato and John Shareshian and Jongbaek Song},
  journal= {arXiv preprint arXiv:2405.09242},
  year   = {2025}
}

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26 pages

Gamma vectors of partitioned permutohedra

Abstract

Keywords

Cite

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