Partitions of large Boolean lattices (Q1332423)

Let \(2^ n\) be the ordered set of all subsets of \(\{1,2,\dots,n\}\) ordered by set inclusion and \(2^ n_ -\) be the ordered set obtained by deleting both the greatest and the least elements from \(2^ n\). Main result (Theorem 2.1): For each positive integer \(m\) and \(n \geq m + 1\), the ordered set \(2^ n_ -\) can be partitioned into antichains of size \(m\) except for at most \(m - 1\) elements which also form an antichain.