Other contributors to the study of unavoidable patterns include van der Waerden. His theorem states that if the positive integers are partitioned into k classes, then there exists a class c such that c contains an arithmetic progression of some unknown length. An arithmetic progression is a sequence of numbers in which the difference between adjacent numbers remains constant. When examining unavoidable patterns sesquipowers are also studied. For some patterns x,y,z, a sesquipower is of the form x, xyx, xyxzxyx, ... This is another pattern such as square-free, or unavoidable patterns. Coudrain and Schützenberger mainly studied these sesquipowers for group theory applications. In addition, Zimin proved that sesquipowers are all unavoidable. Whether the entire pattern shows up, or only some piece of the sesquipower shows up repetitively, it is not possible to avoid it. Necklaces are constructed from words of circular sequences. They are most frequently used in music and astronomy. Flye Sainte-Marie in 1894 proved there are 22"n"−1−"n" binary de Bruijn necklaces of length 2n. A de Bruijn necklace contains factors made of words of length n over a certain number of letters. The words appear only once in the necklace. In 1874, Baudot developed the code that would eventually take the place of Morse code by applying the theory of binary de Bruijn necklaces. The problem continued from Sainte-Marie to Martin in 1934, who began looking at algorithms to make words of the de Bruijn structure. It was then worked on by Posthumus in 1943. Possibly the most applied result in combinatorics on words is the Chomsky hierarchy, developed by Noam Chomsky. He studied formal language in the 1950s. His way of looking at language simplified the subject. He disregards the actual meaning of the word, does not consider certain factors such as frequency and context, and applies patterns of short terms to all length terms. The basic idea of Chomsky's work is to divide language into four levels, or the language hierarchy. The four levels are: regular, context-free, context-sensitive, and computably enumerable or unrestricted. Regular is the least complex while computably enumerable is the most complex. While his work grew out of combinatorics on words, it drastically affected other disciplines, especially computer science. Sturmian words, created by François Sturm, have roots in combinatorics on words.