In theoretical computer science and mathematics, especially in the area of combinatorics on words, the Levi lemma states that, for all strings u, v, x and y, if uv = xy, then there exists a string w such that either uw = x and v = wy (if |u| ≤ |x|) or u = xw and wv = y (if |u| ≥ |x|) That is, there is a string w that is "in the middle", and can be grouped to one side or the other. Levi's lemma is named after Friedrich Wilhelm Levi, who published it in 1944.