Proof of Frankl's Conjecture: A Non-Constructive Approach

Abstract

: Let U be a finite set and X a family of nonempty subsets of U , which is closed under unions. We establish a connection between Frankl's conjecture and equipollence sets, in which a complementary set is an Equipollence set on the Frobenius group. We complete the proof of the union-closed sets using a non-constructive approach. The proof relies upon that we need to prove, that the series of the prime divisor diverges, and there exists x i which appears at least half distributed in subsets.