OpenAI · 169-01 · 2026-09-24 · Combinatorics
Elementary positivity of chromatic quasisymmetric functions
preprints/Elementary-Positivity-of-Chromatic-Quasisymmetric-Functions-September-24-2026
Family 169. The Shareshian–Wachs -positivity conjecture.
The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.
Read against the standing problems
Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N
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 . The coefficients count explicitly described permutations, giving a combinatorial explanation of positivity.
We prove that the chromatic quasisymmetric function of every natural unit interval graph is elementary-positive over . This resolves the elementary-positivity part of the Shareshian–Wachs conjecture.
Preprint source and Lean scope
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This preprint is named in the Lean scope note for 169: Shareshian–Wachs elementary positivity. The authors are OpenAI. This companion does not verify the formalization. It is not a premise. The OAI library is not imported. No compilation is asserted. O.1 stays NOT_CLOSED.