Milliken–Taylor theorem (original) (raw)

In mathematics, the Milliken–Taylor theorem in combinatorics is a generalization of both Ramsey's theorem and Hindman's theorem. It is named after Keith Milliken and Alan D. Taylor. Let denote the set of finite subsets of , and define a partial order on by α<β if and only if max α and k > 0, let Let denote the k-element subsets of a set S. The Milliken–Taylor theorem says that for any finite partition , there exist some i ≤ r and a sequence such that .