Algebraic Combinatorics on Words

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Combinatorics on words has arisen independently within several branches of mathematics, for instance, number theory, group theory and probability, and appears frequently in problems related to theoretical computer science. The first unified treatment of the area was given in Lothaire's Combinatorics on Words. Since its publication, the area has developed and the authors now aim to present several more topics as well as giving deeper insights into subjects that were discussed in the previous volume. An introductory chapter provides the reader with all the necessary background material. There are numerous examples, full proofs whenever possible and a notes section discussing further developments in the area. This book is both a comprehensive introduction to the subject and a valuable reference source for researchers.

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Editorial Reviews

From The Critics
Except for the initial introduction, each of the chapters can be used as a core text for a graduate course. No mathematics beyond a general undergraduate level is assumed, and no exposure to Lothaire's 1983 . Annotation c. Book News, Inc., Portland, OR (
From the Publisher
Review of the hardback: 'This book will certainly become a reference book and have the same impact as the first book of Lotahire: essentially self-contained, with many exercise and interesting notes, not mentioning a bibliography with more than 450 items.' Jean-Paul Allouche, Zentrallblatt MATH

Review of the hardback: '… an indispensable reference …' Mathematika

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Product Details

Table of Contents

Ch. 1 Finite and Infinite Words 1
Ch. 2 Sturmian Words 45
Ch. 3 Unavoidable Patterns 111
Ch. 4 Sesquipowers 135
Ch. 5 The Plactic Monoid 164
Ch. 6 Codes 197
Ch. 7 Numeration Systems 230
Ch. 8 Periodicity 269
Ch. 9 Centralizers of Noncommutative Series and Polynomials 312
Ch. 10 Transformations on Words and q-Calculus 330
Ch. 11 Statistics on Permutations and Words 365
Ch. 12 Makanin's Algorithm 387
Ch. 13 Independent Systems of Equations 443
References 473
Index of Notation 497
General Index 499
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