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arXiv · 1711.07152

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

Soojin Cho·JiSun Huh
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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. The $e$-positivity of chromatic quasisymmetric functions implies the $e$-positivity of corresponding chromatic symmetric functions, and our work resolves Stanley's conjecture on chromatic symmetric functions of $(3+1)$-free posets for two classes of natural unit interval orders.

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Soojin Cho, JiSun Huh. 2017-11-20. On $e$-positivity and $e$-unimodality of chromatic quasisymmetric functions. https://arxiv.org/abs/1711.07152

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