The 11-element case of Frankl's conjecture
Summary: In 1979, \textit{P.Frankl} [Discrete Math. 26, 111--118 (1979; Zbl 0397.05004)] conjectured that in a finite union-closed family \({\mathcal F}\) of finite sets, \({\mathcal F}\neq\{\emptyset\}\), there has to be an element that belongs to at least half of the sets in \({\mathcal F}\). We prove this when \(|\bigcup{\mathcal F}|\leq 11\).
scientific article; zbMATH DE number 5540993