The Width of a set is equal to the minimum number of Chains needed to Cover . Equivalently, if a set of elements is Partially Ordered, then contains a Chain of size or an Antichain of size . Letting be the Cardinality of , the Width, and the Length, this last statement says . Dilworth's lemma is a generalization of the Erdös-Szekeres Theorem. Ramsey's Theorem generalizes Dilworth's lemma.
See also Combinatorics, Erdös-Szekeres Theorem, Ramsey's Theorem