Set families with a forbidden subposet (Q2380308)

Summary: We asymptotically determine the size of the largest family \(\mathcal F\) of subsets of \(\{1,\cdots, n\}\) not containing a given poset \(P\) if the Hasse diagram of \(P\) is a tree. This is a qualitative generalization of several known results including Sperner's theorem.