Solution of a research problem on trees of subsets
Let \(X\) be an \(n\)-element set and \(\mathcal F\) a \(k\)-element collection of proper, non-empty subsets of \(X\) such that if \(A\), \(B\in {\mathcal F}\) then either \(A\subseteq B\), or \(B\subseteq A\), or they are disjoint. A closed formula is given for the number of those collections and it is shown that \(k\leq 2n-2\).
scientific article; zbMATH DE number 646767