In combinatorial mathematics, the union-closed sets conjecture is an elementary problem, posed by Péter Frankl in 1979 and still open. A family of sets is said to be union-closed if the union of any two sets from the family remains in the family. The conjecture states that for any finite union-closed family of finite sets, other than the family consisting only of the empty set, there exists an element that belongs to at least half of the sets in the family.
Read more about Union-closed Sets Conjecture: Equivalent Forms, Families Known To Satisfy The Conjecture, History
Famous quotes containing the words sets and/or conjecture:
“Nothing sets a person up more than having something turn out just the way it’s supposed to be, like falling into a Swiss snowdrift and seeing a big dog come up with a little cask of brandy round its neck.”
—Claud Cockburn (1904–1981)
“There is something fascinating about science. One gets such wholesale returns of conjecture out of such a trifling investment of fact.”
—Mark Twain [Samuel Langhorne Clemens] (1835–1910)