Set families with a forbidden induced subposet

الأصل · EN

For each poset H whose Hasse diagram is a tree of height k, we show that the largest size of a family of subsets of [n]={1,..., n} not containing H as an induced subposet is asymptotic to (k-1)n n/2. This extends the result of Bukh bukh, which in turn generalizes several known results including Sperner's theorem.