Sperner system

Let P be a finite partially ordered set, then an antichain in P is a set of pairwise incomparable elements. Antichains are also called Sperner systems in older literature. For example, consider P to be a family of subsets together with the subset relation (i.e., s_1<=s_2 if s_1 is a subset of s_2). The following table gives the antichains on the set of subsets (i.e., the power set) of the n-set {1, 2, 3, ..., n} for small n.

Boolean function | chain | Dedekind number | Dedekind's problem | Dilworth's lemma | partially ordered set | partial order width

Richard Dedekind