Combinatorics on words is a branch of mathematics which applies combinatorics to words and formal languages. The study of combinatorics on words arose independently within several branches of mathematics, e.g. number theory, group theory and probability. It has applications to combinatorial enumeration and fractal analysis and appears in problems of theoretical computer science, automata theory and linguistics. While many applications are new, the classical Chomsky–Schutzenberger hierarchy of classes of formal grammars is perhaps the best known result in the field. The development of computerized text and string processing has led to important applications of combinatorics on words. It is involved in the core algorithms for text processing, natural language processing, speech processing and bioinformatics. The study of combinatorics of words goes back to the works of Axel Thue on nonrepetitive sequences of symbols at the beginning of the 20th century.

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