Stanley's Rankwise Lower-Bound Conjecture for Differential Posets
Must every -differential poset have at least as many elements in each rank as , the -th Cartesian power of Young's lattice? For the new construction has fourth-rank size against for .
- Result
- Disproved
- Status
- Resolved
- AI contribution
- AI-discovered
- Method
- Construction
- Field
- Differential posets
- Posed by
- Richard Stanley
- Year posed
- 1988
- Years open
- 38y
- Solved
- 2026-07-28
- Model
- TARS agent system
- Vendor
- —
- Collaborators
- —
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 15 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
The counterexample was generated by the TARS agent system (underlying foundation model not disclosed) through autonomous mathematical search, then examined and independently verified by the human authors.
Verification
Explicit construction verified by the human authors and published as an arXiv preprint. Not yet peer-reviewed.
Source
arXiv:2607.22988 - An explicit counterexample to Stanley's rankwise lower-bound conjecture