Powers of the Vandermonde Determinant Are Eventually Non-SNP
Monical, Tokcan and Yong conjectured that every fixed positive power of the Vandermonde determinant fails to have saturated Newton polytope in sufficiently many variables. For every even power there is an explicit lattice point of the Newton polytope of with vanishing coefficient, obtained from a Dyson constant-term identity; the odd case follows by alternation, proving the conjecture.
- Result
- Proved
- Status
- Resolved
- AI contribution
- AI-discovered
- Method
- Construction
- Field
- Algebraic combinatorics
- Posed by
- Cara Monical, Neriman Tokcan, Alexander Yong
- Year posed
- 2017
- Years open
- 9y
- Solved
- 2026-07-26
- Model
- Codex (GPT-5.6 Sol Extra High)
- Vendor
- OpenAI
- Collaborators
- Thien Le, Melanie Weber
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 15 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
The key even-power construction and the proof strategy arose from prompting OpenAI Codex; the complete transcript appears in the paper's appendix. The authors subsequently checked and organized the argument.
Verification
arXiv preprint with the prompting transcript in an appendix and an accompanying Lean formalization (coverage per its repository); not yet peer-reviewed.
Sources
arXiv:2607.23828 - Powers of the Vandermonde determinant are eventually non-SNP