On 05.06.2012 at 12:20 in S8, there is the following noon lecture:
Supersaturation in the Boolean Lattice
Jerrold R. Griggs
University of South Carolina
(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.
Modified: 19. 10. 2010