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.
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