An Asymptotic Version of Frankl’s Conjecture

Abstract

We show that the maximum average set size in complements of union-closed families over n elements is $(n+1)/2$. This implies an asymptotic version of Frankl’s conjecture.

Keywords:

• MSC: Primary 05A20

Acknowledgments

I would like to thank Sebastian Baader, Livio Liechti, Ilan Karpas, and the two referees for valuable comments, as well as Susan Jane Colley for her help in preparing this note.