Resolves the elementary-positivity part of the Shareshian–Wachs conjecture: the chromatic quasisymmetric function of every natural unit interval graph has elementary-basis coefficients in \mathbb N[q]. The coefficients count explicitly described permutations, giving a combinatorial explanation of positivity. (Lean)
Manuscript
Elementary positivity of chromatic quasisymmetric functions
September 24, 2026 · source · cite as \cite{OAI:Elementary-Positivity-of-Chromatic-Quasisymmetric-Functions-September-24-2026}
We prove that the chromatic quasisymmetric function of every natural unit interval graph is elementary-positive over \mathbb N[q]. This resolves the elementary-positivity part of the Shareshian–Wachs conjecture.
Result 169 · Combinatorics. Imported from openai/math, a collection of manuscripts produced by an OpenAI model; results are at different stages of verification. Discussion below is by Lemma members.
Source: https://github.com/openai/math/blob/main/CONTENTS.md