Power Sum Expansion of Chromatic Quasisymmetric Functions
Keywords:
Graph coloring, Quasisymmetric function, Power sum symmetric function, Interval order, Descent, Acyclic orientation
Abstract
The chromatic quasisymmetric function of a graph was introduced by Shareshian and Wachs as a refinement of Stanley's chromatic symmetric function. An explicit combinatorial formula, conjectured by Shareshian and Wachs, expressing the chromatic quasisymmetric function of the incomparability graph of a natural unit interval order in terms of power sum symmetric functions, is proven. The proof uses a formula of Roichman for the irreducible characters of the symmetric group.