Real-Rootedness of Ehrhart h*-Polynomials at Large Width
A question of Averkov, Hofscheier and Nill on whether the Ehrhart -polynomial of a lattice polytope of large lattice width is real-rooted. Proved in fixed dimension for sufficiently large lattice width, giving strict log-concavity and unimodality of the -vector, with the analogous statement for the local -polynomial of a lattice simplex.
- Result
- Proved
- Status
- Resolved
- AI contribution
- AI-discovered
- Method
- Argument
- Field
- Polyhedral combinatorics
- Posed by
- Gennadiy Averkov, Johannes Hofscheier, Benjamin Nill
- Year posed
- 2023
- Years open
- 3y
- Solved
- 2026-08-04
- Model
- ChatGPT 5.6 Sol
- Vendor
- OpenAI
- Collaborators
- Benjamin Nill
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 15 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
The acknowledgments state that the proofs were found using ChatGPT 5.6 Sol, which also produced a first draft of the paper, with the author solely responsible for the final version.
Verification
arXiv preprint, not yet peer-reviewed.