Combinatorics on words, or finite sequences, is a field which grew simultaneously within disparate branches of mathematics such as group theory and probability. It has grown into an independent theory finding substantial applications in computer science automata theory and linguistics. This volume is the first to attempt to present a thorough treatment of this theory. All of the main results and techniques are covered. The presentation is accessible to undergraduate and graduate level students in mathematics and computer science as well as to specialists in all branches of applied mathematics. Topics discussed include: Thue's square free words, Van der Waerden's theorem, Ramsey's theorem; factorization of free monoids including application to free Lie algebras; equations in words, etc.

• Classic book • Subject remains important • Very affordable paperback

### Contents

1. Words D. Perrin; 2. Square free words and idempotent semigroups J. Berstel and C. Reutenauer; 3. Van der Waerden's theorem J. E. Pin; 4. Repetitive mappings and morphisms G. Pirillo; 5. Factorizations of free monoids D. Perrin; 6. Subwords J. Sakarovitch and I. Simon; 7. Unavoidable irregularities in words M. P. Schützenberger; 8. The critical factorization theorem Choffrut; 9. Equations in words; 10. Rearrangements of words D. Foata; 11. Words and trees R. Cori.

### Reviews

' … a thorough treatment of the theory of combinatorics.' Monatshefte für Mathematik

'Since the first edition almost fifteen years ago, a new generation of young mathematicians has grown up on reading this book and solving the problems at the end of each chapter, thus deepening the understanding of the results read, analyzing special cases and proving additional results. Furthermore, this monograph is an excellent reference book for those working in this area of mathematics.' Acta Sci. Math.

'This is an excellent book, essential for anybody working in the field. Although written by several authors, who constitute the collective author M. Lothaire, the book makes a surprisingly compact impression. As already mentioned, it has all prerequisites for an important reference tool.' EMS