# Noon lecture

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On 10.1.2013 at 12:20 in S6, there is the following noon lecture:

# Union-Closed Families of Sets

## Béla Bollobás

## Cambridge and Memphis

## Abstract

A family of sets is union-closed if it contains the union of any two of its elements. Much of the interest in union-closed families is due to the notorious union-closed conjecture, which states that for every union-closed family of m sets there is an element in at least m/2 of the sets. In the talk I shall review some of the results about union-closed families, and present some of the results I have proved with Eccles and Balla about the average size of a set in such a family with m members.

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