The kernel of chromatic quasisymmetric functions on graphs and hypergraphic polytopes

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.