## The Chromatic Quasisymmetric Functions of Directed Graphs

- Oct. 28, 2016
- 2:30 p.m.
- LeConte 312

## Abstract

The chromatic symmetric functions were introduced by Richard Stanley as a symmetric function analog of the chromatic polynomials. A long standing conjecture of Stanley and Stembridge asserts that for a class of graphs that include unit interval graphs, the chromatic symmetric function has positive coefficients when expanded in the basis of elementary symmetric functions. A refinement of this conjecture was given by Shareshian and Wachs involving their chromatic quasisymmetric functions. We present a generalization of the Shareshian-Wachs refinement to a larger class of graphs, namely proper circular arc graphs. We discuss results on expansions of the chromatic quasisymmetric functions of this larger class in the power sum and elementary bases, which generalize work of Stanley, Shareshian-Wachs, and Athanasiadis. No prior knowledge of symmetric functions is needed for this talk.