Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: Family 169. The Shareshian–Wachs e -positivity conjecture
Family claims › Combinatorics · lines 1177–1182
OpenAI@2026-10-07#rem:oai-169
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.
The authors are OpenAI. This companion does not verify the proof. The claim is not a theorem of the Enter series and not a premise of any registered sheet. It does not close O.1. O.1 stays NOT_CLOSED. It is not a de Sitter state and not the QdS external-leg scheme. No quantum coefficient is admitted. No compilation is asserted.
Nearby in this section
- remark: Remark: Family 155. A counterexample to periodic tiling in dimension three
- remark: Remark: Family 156. Borsuk's conjecture fails in dimension nine
- remark: Remark: Family 157. Counterexamples to the Hadwiger and Colin de Verdi conjectures
- remark: Remark: Family 158. The Euclidean plane cannot be colored with five colors
- remark: Remark: Family 159. Erd (o)s's reciprocal-sum conjecture and quasipolynomial Szemerédi bounds
- remark: Remark: Family 160. Superexponential van der Waerden numbers
- remark: Remark: Family 161. Counterexamples to Sidorenko's conjecture and the forcing conjecture
- remark: Remark: Family 162. Counterexamples to Ryser's covering and Gyárfás's tree-cover conjectures