MATH Seminar

Title: An Erdos-Ko-Rado Theorem for cross t-intersecting families
Seminar: Combinatorics
Speaker: Sang June Lee of Duksung Women's University
Contact: Vojtech Rodl, Rodl@mathcs.emory.edu
Date: 2015-01-12 at 4:00PM
Venue: MSC E406
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Abstract: A central result in extremal set theory is `the Erdos-Ko-Rado Theorem' (1961) which investigates the maximum size of families X of k-subsets in [n] such that two members in X intersect with at least t elements.\\ \\ Two families X and Y of k-subsets in [n] are called `cross t-intersecting' if, for every members A in X and B in Y, we have that A and B intersect with at least t elements. The cross t-intersecting version of the Erdos-Ko-Rado Theorem was conjectured but still open.\\ \\ In this talk we verify the conjecture for all integers t>13 except finitely many n and k for each fixed t. Our proofs make use of a weight version of the problem and randomness. This is joint work with Peter Frankl, Norihide Tokushige, and Mark Siggers.