Gamma Vectors of Partitioned Permutohedra

  • Tatsuya Horiguchi
  • Mikiya Masuda
  • Takashi Sato
  • John Shareshian
  • Jongbaek Song
DOI: https://doi.org/10.37236/14561

Abstract

We show that $\gamma$-vectors of partitioned permutohedra have nonnegative entries, thereby generalizing a result of Foata and Schützenberger. 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.

Published
2026-09-11
How to Cite
Horiguchi, T., Masuda, M., Sato, T., Shareshian, J., & Song, J. (2026). Gamma Vectors of Partitioned Permutohedra. The Electronic Journal of Combinatorics, 33(3), #P3.61. https://doi.org/10.37236/14561
Issue
Volume 33, Issue 3 (2026)
Article Number
P3.61