Lothaire M. Combinatorics on Words

Cambridge University Press, 1997, -254 p.This is the first book devoted to broad study of the combinatorics of words, that is to say, of sequences of symbols called letters. This subject is in fact very ancient and has cropped up repeatedly in a wide variety of contexts. Even in the most elegant parts of abstract pure mathematics, the proof of a beautiful theorem surprisingly often reduces to some very down to earth combinatorial lemma concerning linear arrays of symbols. In applied mathematics, that is in the subjects to which mathematics can be applied, such problems are even more to be expected. This is true especially in those areas of contemporary applied mathematics that deal with the discrete and non-commutative aspects of the world about us, notably the theory of automata, information theory, and formal linguistics.Words
Square-Free Words and Idempotent Semigroups
Van der Waerden's Theorem
Repetitive Mappings and Morphisms
Factorizations of Free Monoids
Subwords
Unavoidable Regularities in Words and Algebras with Polynomial Identities
The Critical Factorization Theorem
Equations in Words
Rearrangements of Words
Words and Trees