A family of sets is said to be union-closed if the union of any two sets from the family remains in the family. Franklâ€™s conjecture, aka the union-closed sets conjecture, is the remarkable statement that for any finite union-closed family of finite sets, there exists an element that belongs to at least half of the sets in the family. Originally stated in 1979, it is still wide open. This will be an informal discussion on progress towards the conjecture.

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Last updated: 24 Mar 2023