# Noon lecture

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On 5.6.2012 at 12:20 in S8, there is the following noon lecture:

# Supersaturation in the Boolean Lattice

## Jerrold R. Griggs

## University of South Carolina

## Abstract

(joint work with J.S.Sereni and Ross Kang)

If one has a collection F of subsets of the n-set [n], one can ask how many pairs of subsets A, B ("edges") must there be in F with A contained in B? We show that if |F|=C(n,n/2) +x, then there are at least xf edges, where f is \lceil (n+1)/2 \rceil, which is best-possible for small x. We are trying to solve the problem for general |F| of minimizing the number of edges in F. This would then recover a result of Kleitman(1966) that proves a conjecture of Erdos and Katona, and we hope to prove its generalization proposed by Kleitman.

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