Pak-Slonim Conjecture on Stretched Schubert Structure Constants
Pak and Slonim conjectured that stretched Schubert structure constants are eventually polynomial. They are. Monomial coefficients in affine families of key and Schubert polynomials are eventually polynomial, and the Schubert duality of Watanabe carries this to the structure constants. The same result settles the polynomiality half of a conjecture of Alexandersson and Alhajjar for key polynomials.
- Result
- Proved
- Status
- Resolved
- AI contribution
- AI-assisted
- Method
- Argument
- Field
- Algebraic combinatorics
- Posed by
- Igor Pak, Zachary Slonim
- Year posed
- 2026
- Years open
- 0y
- Solved
- 2026-07-21
- Model
- Codex
- Vendor
- OpenAI
- Collaborators
- Per Alexandersson
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 15 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
The acknowledgement says only that Codex was used during preparation of the paper for proof exploration and editorial assistance. The two are not separated and no step is attributed, so the lowest tier applies.
Verification
Single-author arXiv preprint; not yet peer-reviewed.