Zoltan Füredi (Rényi Institute, Budapest, Hungary and UIUC)
An introduction to the delta system method
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Abstract: Let m(n,3,{0,1}) denote the maximum size of a triple system on n elements. One can easily show that m \leq n(n-1)/6, and here equality holds only for a Steiner Triple System. We give a short introduction to the delta system method in extremal hypergraph theory and prove, e.g., that m(n,7,{0,1,3}) \leq n(n-1)(n-3)/168 (for n>n_0) and here equality holds, e.g., for n=2^d-1. In other words, we want to determine the maximum size of a 7-uniform hypergraph H on n elements such that every two hyperedges of H are either disjoint or have intersection in 1 or 3 elements.
