Abigail Raz, Rutgers University

Abstract

The union-closed sets conjecture states that for any union closed family of sets with only finitely many member sets (and not only the empty set) there is an element appearing in at least half the sets. In this talk we will discuss a few weaker results that hold for union closed families motivated by the conjecture. Additionally, time permitting we will discuss a few reformulations of the conjecture in the language of lattices and graphs. We will state, and maybe even prove, that the conjecture is true for certain families.