Problem dossier · Graph Theory
Frankl's union-closed sets conjecture
In every finite union-closed family of sets (other than {∅}), some element belongs to at least half of the sets.
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Status
Open. Gilmer's 2022 information-theoretic breakthrough gives a universal constant ≈ 0.38 (improved toward the golden-ratio bound ≈ 0.382); the 1/2 target stands.
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The Angle of Attack
Enumerate small union-closed families hunting for anything below 1/2; probe the tightness of the entropy method's constant with structured families.
Tags: set families · union-closed · entropy · extremal
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The Lab
No instruments built yet. When this problem gets tackled, its interactive instruments — explorers, searches, verifiers running in the browser — live here. See the Collatz dossier for what a fully tackled problem looks like.
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The Log
Empty. Work on this problem gets logged here as dated entries — constructions tried, code run, dead ends included. Dead ends are results.
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