Reiner's Conjecture on Higher Bruhat Orders in Corank 3
Reiner conjectured a description of the homotopy types of intervals in higher Bruhat orders. In corank it holds: the facial intervals of are exactly the spherical intervals, and every other interval is contractible.
- Result
- Proved(see note)
- Status
- Partial result
- AI contribution
- AI-assisted
- Method
- Argument
- Field
- Algebraic combinatorics
- Posed by
- Victor Reiner
- Year posed
- —
- Years open
- —
- Solved
- 2026-07-23
- Model
- ChatGPT Pro (5.5, 5.6 Sol)
- Vendor
- OpenAI
- Collaborators
- Daria Poliakova
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 10 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What was actually shown
corank 3; the general conjecture remains open, corank 2 being McConville's case
What the AI did
The AI use declaration lists the model as search engine, proof assistant, vector graphics artist and editor, and states that all outputs of the proof assistant were thoroughly digested by a human and that the exposition is by and for humans.
Verification
Single-author arXiv note; not yet peer-reviewed.
Source
arXiv:2607.21420 - Homotopy types of intervals in corank-three higher Bruhat orders