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- En mathématiques, et plus précisément en combinatoire, la conjecture des familles stables par unions est un problème d'énoncé élémentaire posé par Péter Frankl en 1979 et toujours ouvert. Une famille d'ensembles est dite stable par unions si l'union de deux ensembles quelconque de la famille est encore dans la famille. La conjecture affirme que pour toute famille finie d'ensembles finis (non vides), stable par unions, il existe un élément appartenant à au moins la moitié des ensembles de la famille. (fr)
- In combinatorics, the union-closed sets conjecture is a problem, posed by Péter Frankl in 1979 and is still open. 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 family containing only the empty set, there exists an element that belongs to at least half of the sets in the family. Professor Timothy Gowers called this "one of the best known open problems in combinatorics" and 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 ..." (en)
- Гипотеза Франкла — гипотеза в комбинаторике, известная как открытая задача с элементарной формулировкой. (ru)
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- En mathématiques, et plus précisément en combinatoire, la conjecture des familles stables par unions est un problème d'énoncé élémentaire posé par Péter Frankl en 1979 et toujours ouvert. Une famille d'ensembles est dite stable par unions si l'union de deux ensembles quelconque de la famille est encore dans la famille. La conjecture affirme que pour toute famille finie d'ensembles finis (non vides), stable par unions, il existe un élément appartenant à au moins la moitié des ensembles de la famille. (fr)
- Гипотеза Франкла — гипотеза в комбинаторике, известная как открытая задача с элементарной формулировкой. (ru)
- In combinatorics, the union-closed sets conjecture is a problem, posed by Péter Frankl in 1979 and is still open. 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 family containing only the empty set, there exists an element that belongs to at least half of the sets in the family. (en)
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- Conjecture des familles stables par unions (fr)
- Гипотеза Франкла (ru)
- Union-closed sets conjecture (en)
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