Department of Mathematics
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Frankl's conjecture says that for \(S\) a non-empty set and \(U\) a finite subset of the set of all subsets of \(S\) such that for \(A\), \(B\) in \(U\), the set union of \(A\) and \(B\) is also in \(U\) (that is, \(U\) is a union closed set), we can always find some \(s \in S \) such that the number of members of \( U \) containing \( s \) is at least half the number of all members of \( U\).

A union closed set is an example of a finite semilattice, with set union as the semilattice operation. In this talk, I will present an attempt to prove Frankl's conjecture by a detailed analysis of the structure of finite semilattices.