Ehrhart Positivity of Schubitopes
Monical, Tokcan and Yong conjectured that Schubitopes, the generalized permutahedra arising as Newton polytopes of Schubert polynomials and of Demazure characters of , are Ehrhart positive. Disproved by an explicit Schubitope whose Ehrhart polynomial has a negative coefficient in its monomial expansion.
- Result
- Disproved
- Status
- Resolved
- AI contribution
- AI-discovered
- Method
- Construction
- Field
- Algebraic combinatorics
- Posed by
- Cara Monical, Neriman Tokcan, Alexander Yong
- Year posed
- 2019
- Years open
- 7y
- Solved
- 2026-08-01
- Model
- GPT-5.6 Sol Pro
- Vendor
- OpenAI
- Collaborators
- Yupeng Li, Avery St. Dizier
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 15 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
The abstract states the counterexample was found using GPT-5.6 Sol Pro in ChatGPT. The authors supply the surrounding treatment of the family.
Verification
arXiv preprint; not yet peer-reviewed. The result is a single explicit polytope, so it is checkable by direct computation.
Source
Submitted by Curator34