A proof of the Stanley--Stembridge conjecture

TL;DR

This paper provides a probabilistic interpretation of certain symmetric function coefficients and uses this to prove the long-standing Stanley--Stembridge conjecture in graph theory.

Contribution

It introduces a novel probabilistic approach to understanding chromatic quasisymmetric functions and proves the Stanley--Stembridge conjecture for all unit interval graphs.

Findings

Probabilistic interpretation of elementary symmetric function coefficients

Proof of the Stanley--Stembridge conjecture for unit interval graphs

Enhanced understanding of chromatic quasisymmetric functions

Abstract

We give a probabilistic interpretation of the coefficients of the elementary symmetric function expansion of the chromatic quasisymmetric function for any unit interval graph. As a corollary, we prove the Stanley--Stembridge conjecture.