Diamond-free families

Given a finite poset P, we consider the largest size La(n,P) of a family of subsets of [n]:={1,…,n} that contains no (weak) subposet P. This problem has been studied intensively in recent years, and it is conjectured that exists for general posets P, and, moreover, it is an integer. For k⩾2 let Dk denote the k-diamond poset {A