On families of subsets with a forbidden subposet

Linyual Lincoln Lu

ABSTRACT: Let F&sub 2^[n] be a family of subsets of [n]={1,2, ..., n}. For any poset H, we say F is H-free if F does not contain any subposet isomorphic to H. For a fixed poset H, let La(n,H) be the maximum size of H-free families F&sub 2^[n]. We give bounds on La(n,H) in terms of H.