Combinatorics·OpenAI Math·Result 169·Lean formalisation listed
Shareshian–Wachs elementary positivity
One of the 372 results in OpenAI's public mathematics catalogue, filed under combinatorics: 1 preprint, the latest dated 24 September 2026. This page quotes OpenAI's own summary of the claim, links the paper and abstract, and will embed the animation.
Latest paper
Elementary positivity of chromatic quasisymmetric functions
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What OpenAI claims
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 ℕ[q]. The coefficients count explicitly described permutations, giving a combinatorial explanation of positivity. (Lean)
Paper
Elementary positivity of chromatic quasisymmetric functions
We prove that the chromatic quasisymmetric function of every natural unit interval graph is elementary-positive over ℕ[q]. This resolves the elementary-positivity part of the Shareshian–Wachs conjecture.
Status
Preprint. The paper has not been independently reviewed. Treat the result as OpenAI's claim until other mathematicians have checked it. If a video exists, it illustrates the statement; it is not the proof.
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