The maximal length of cloud-antichains (Q1332440)

The notion of an antichain of a partially ordered set can be generalized to that of cloud-antichain, where subsets take the role of incomparable elements. In fact, there are six possibilities to define cloud- antichains. The authors study especially cloud-antichains of the power set of the set \(\{1,2,\dots, n\}\) that is partially ordered by inclusion. They give asymptotically maximal lengths of cloud-antichains for all six cases. For three of them, they give exact results.