Séminaire Lotharingien de Combinatoire, 80B.59 (2018), 12 pp.

Soojin Cho and JiSun Huh

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 e-positivity and the e-unimodality of these functions. Our work resolves the Stanley's conjecture on chromatic symmetric functions of (3+1)-free posets for two classes of natural unit interval orders.

Received: November 14, 2017. Accepted: February 17, 2018. Final version: April 1, 2018.

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