Gamma vectors of partitioned permutohedra
Tatsuya Horiguchi, Mikiya Masuda, Takashi Sato, John Shareshian,, Jongbaek Song
TL;DR
This paper investigates the gamma-vectors of partitioned permutohedra, extending previous results and connecting them to symmetric group representations on permutohedral variety cohomology.
Contribution
It generalizes Foata and Schützenberger's result on gamma-vectors and links it to Athanasiadis' work on symmetric group actions.
Findings
Gamma-vectors of partitioned permutohedra are explicitly determined.
The results unify and derive Athanasiadis' findings from the gamma-vector perspective.
Provides a new combinatorial interpretation of symmetric group representations.
Abstract
We determine that -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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Combinatorial Mathematics · Advanced Algebra and Geometry