Combinatorics on Words: Christoffel Words and Repetitions in Words
American Mathematical Soc. - Mathematics - 147 pages
The two parts of this text are based on two series of lectures delivered by Jean Berstel and Christophe Reutenauer in March 2007 at the Centre de Recherches Mathematiques, Montreal, Canada. Part I represents the first modern and comprehensive exposition of the theory of Christoffel words. Part II presents numerous combinatorial and algorithmic aspects of repetition-free words stemming from the work of Axel Thue - a pioneer in the theory of combinatorics on words.
A beginner to the theory of combinatorics on words will be motivated by the numerous examples, and the large variety of exercises, which make the book unique at this level of exposition. The clean and streamlined exposition and the extensive bibliography will also be appreciated. After reading this book, beginners should be ready to read modern research papers in this rapidly growing field and contribute their own research to its development.
Experienced readers will be interested in the finitary approach to Sturmian words that Christoffel words offer, as well as the novel geometric and algebraic approach chosen for their exposition. They will also appreciate the historical presentation of the Thue-Morse word and its applications, and the novel results on Abelian repetition-free words.
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alphabet automaton balanced1 begin binary words Cayley graph Chapter Christoffel morphisms Christoﬀel path Christoffel tree Christoﬀel word conjugate construction contains a square context-free grammar context-free language continued fraction representation Corollary Crochemore factorization ct(n deﬁned Deﬁnition denote Example Exercise exists factors of length Fibonacci word Figure ﬁnd ﬁrst ﬁxed follows free group Han(n Hint inﬁnite word inﬁx integer points labelled left special factor letters line segment linear lower Christoﬀel Lyndon word magic square monoid morphism h Morse word node nonempty overlap-free Pal(w palindrome path from 0,0 positive integers preﬁx Proof Proposition Prove recurrent regular language relatively prime segment from 0,0 sequence slope b/a square-free words standard factorization Sturmian words suffix suﬃx tree Suppose Theorem Three Squares Lemma Thue Thue–Morse word Tower of Hanoi upper Christoffel word word of length word of slope Zimin word