The kernel of chromatic quasisymmetric functions on graphs and hypergraphic polytopes

TL;DR

This paper characterizes the kernel of chromatic quasisymmetric functions on graphs and hypergraphic polytopes, revealing modular relations and proposing new graph invariants to address the tree conjecture.

Contribution

It generalizes the kernel description from graphs to hypergraphic polytopes and introduces new invariants for tackling the tree conjecture.

Findings

Kernel of chromatic symmetric function spanned by modular relations

Generalization to hypergraphic polytopes

Identification of new graph invariants

Abstract

We study the chromatic symmetric function on graphs, and show that its kernel is spanned by the modular relations. We generalize this result to the chromatic quasisymmetric function on hypergraphic polytopes, a family of generalized permutahedra. We use this description of the kernel of the chromatic symmetric function to find other graph invariants that may help us tackle the tree conjecture.