Stanley's Problem 4 on Differential Posets
For a differential poset , must the weighted -multichain series be a rational multiple of , the square of its rank generating series?
- 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 construction was found by the TARS agent system (foundation model not disclosed); the proof was reconstructed and manually verified by the human authors.
Verification
A locally finite -differential poset with nonrational quotient series over every characteristic-zero field; the construction yields continuum many such series. Author-verified arXiv preprint, not yet peer-reviewed.
Source
arXiv:2607.24541 - A negative answer to Stanley's Problem 4 on differential posets