On e-positivity and e-unimodality of chromatic quasisymmetric functions

Abstract

The e-positivity conjecture and the e-unimodality conjecture of chromatic quasisymmetric functions are proved for some classes of natural unit interval orders. Recently, J. Shareshian and M. Wachs introduced chromatic quasisymmetric functions as a refinement of Stanley's chromatic symmetric functions and conjectured the epositivity and the e-unimodality of these functions. Our work resolves the Stanley's conjecture on chromatic symmetric functions of p3 ` 1q-free posets for two classes of natural unit interval orders.