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Union-closed sets conjecture — Wikipedia (en)

Source: Wikipedia (en)
Original: https://en.wikipedia.org/wiki/Union-closed_sets_conjecture
License (as archived): CC-BY-SA-4.0
Archived: 2026-10-07T17:38:18.620Z
SHA-256 of the archived text: 9db273c9eaa910906c57de4eef60254a3d9ba3b56f04670040ef6ff95044bed7
Stable URL of this page: https://metraipolis.com/documento/dc_fe573ff9e024

How to cite

Union-closed sets conjecture — Wikipedia (en) — Wikipedia (en), https://en.wikipedia.org/wiki/Union-closed_sets_conjecture (CC-BY-SA-4.0); archived copy: https://metraipolis.com/documento/dc_fe573ff9e024 (Metraipolis archive dc_fe573ff9e024, sha256 9db273c9eaa910906c57de4eef60254a3d9ba3b56f04670040ef6ff95044bed7)

BibTeX

@misc{dcfe573ff9e024,
  title = {Union-closed sets conjecture — Wikipedia (en)},
  howpublished = {Wikipedia (en)},
  url = {https://en.wikipedia.org/wiki/Union-closed_sets_conjecture},
  note = {License CC-BY-SA-4.0; archived copy https://metraipolis.com/documento/dc_fe573ff9e024; sha256 9db273c9eaa910906c57de4eef60254a3d9ba3b56f04670040ef6ff95044bed7},
  year = {2026}
}

Archived text

Reproduced under CC-BY-SA-4.0. Attribution: Wikipedia (en), https://en.wikipedia.org/wiki/Union-closed_sets_conjecture. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

The union-closed sets conjecture, also known as Frankl’s conjecture, is an open problem in combinatorics posed by Péter Frankl in 1979. A family of sets is said to be union-closed if the union of any two sets from the family belongs to the family. The conjecture states: For every finite union-closed family of sets, other than the empty family, there exists an element that belongs to at least half of the sets in the family. Professor Timothy Gowers has called this "one of the best known open problems in combinatorics" and has said that the conjecture "feels as though it ought to be easy (and as a result has attracted a lot of false proofs over the years). A good way to understand why it isn't easy is to spend an afternoon trying to prove it. That clever averaging argument you had in mind doesn't work ..."

Tema degli esploratori: matematica e informatica teorica (deposito sistematico; ricerca «combinatorics»).
Fonte: Wikipedia in inglese, voce «Union-closed sets conjecture» — https://en.wikipedia.org/wiki/Union-closed_sets_conjecture
Wikidata Q2993338 (dati Wikidata in CC0 1.0) — https://www.wikidata.org/wiki/Q2993338
Autori: i contributori di Wikipedia (cronologia: https://en.wikipedia.org/wiki/Union-closed_sets_conjecture?action=history).
Licenza: Creative Commons Attribuzione-Condividi allo stesso modo 4.0 (CC BY-SA 4.0) — https://creativecommons.org/licenses/by-sa/4.0/. Il riuso richiede attribuzione e stessa licenza.
Estratto dell'introduzione non modificato nel contenuto; revisione 1350313043, consultata il 2026-10-07T17:08:28.111Z tramite l'API ufficiale di Wikipedia. Impronta SHA-256 dell'estratto: 709683d54e1c9e74986cfe90b610a95f53a3c6dc011b0f63d891347d9d51d4d4