Let G be a hypergraph (set system) on X and S be a subset of X. The trace of G on S is defined as G|S = { E ∩ S: E ∈ G }. We say that G contains another hypergraph H as a trace if G|S contains a copy of H for some set S. Consider the following extremal problem: how many edges can an r-uniform hypergraph on [n] have without containing H as a trace? We give recent results when H is a power set or a complete uniform hypergraph.
This is a joint work with Dhruv Mubayi.