Combinatorics on words

Summary

Combinatorics on words studies finite and infinite sequences of letters from an alphabet, see the definition. Typical topics are repetitions such as squares and overlaps, periodicity, unavoidable patterns, and the number of distinct factors of a word. Classical objects of the field are the Thue–Morse sequence and the de Bruijn sequences. It has links with algebra through the free monoid of words, with number theory, and with the theory of formal languages.