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Frankl's union-closed sets conjecture
Prove that some element lies in at least half the sets of every union-closed family; the best proven fraction is about 0.38.
| 1 | { |
| 2 | "domain": "mathematics", |
| 3 | "topics": [ |
| 4 | "combinatorics" |
| 5 | ], |
| 6 | "type": "proof", |
| 7 | "also": [ |
| 8 | "construction" |
| 9 | ], |
| 10 | "source": { |
| 11 | "key": "optimization-constants", |
| 12 | "name": "Optimization Constants in Mathematics", |
| 13 | "url": "https://teorth.github.io/optimizationproblems/constants/6a.html", |
| 14 | "id": "6", |
| 15 | "curator": "Terence Tao and contributors", |
| 16 | "poser": "Péter Frankl", |
| 17 | "status": "open", |
| 18 | "as_of": "2026-10-20", |
| 19 | "catalog": "0521c19bbd38" |
| 20 | }, |
| 21 | "review": true, |
| 22 | "approval": "first-time" |
| 23 | } |