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Acyclic orientations and Hessenberg varieties

Jean-Christophe Novelli, Jean-Yves Thibon

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.

Acyclic orientations and Hessenberg varieties

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.
Paper Structure (5 sections, 2 equations)

This paper contains 5 sections, 2 equations.

Table of Contents

  1. Introduction
  2. Background
  3. Chromatic quasi-symmetric functions
  4. Dyck graphs
  5. Hessenberg varieties