English

Acyclic orientations and Hessenberg varieties

Combinatorics 2024-01-23 v1

Abstract

We exhibit a bijection between acyclic orientations of a Dyck graph and Tymoczko cells of a regular nilpotent Hessenberg variety. This implies the Shareshian-Wachs formula for the sum of the coefficients of the chromatic quasi-symmetric function of a Dyck graph in the elementary basis.

Keywords

Cite

@article{arxiv.2401.11165,
  title  = {Acyclic orientations and Hessenberg varieties},
  author = {Jean-Christophe Novelli and Jean-Yves Thibon},
  journal= {arXiv preprint arXiv:2401.11165},
  year   = {2024}
}

Comments

6 pages

R2 v1 2026-06-28T14:22:21.966Z