Combinatorics on words. Christoffel words and repetitions in words.

*(English)*Zbl 1161.68043CRM Monograph Series 27. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4480-9/hbk). xii, 147 p. $ 51.00 (2009).

This monograph is based on lectures presented during the school on “Combinatorics on Words”, held in March 2007 at the Centre de recherches mathématiques, Montréal, Canada. The monograph is divided into two independent parts.

The first part gives a self-contained review of results on Christoffel words and their applications. Christoffel words are defined as codes of monotonic paths in discrete plane or equivalently as cycles in Cayley graphs of groups $\mathcal{Z}/(a+b)\mathcal{Z}$, where $a,b$ are relatively prime.

In the second part, there are presented some recent results on combinatorics on words that deal with repetition in special classes of words. Special attention is paid to properties and applications of Thue-Morse words.

Reviewer: Ludovit Niepel (Safat)

##### MSC:

68R15 | Combinatorics on words |

05E20 | Group actions on designs, etc. (MSC2000) |

05-02 | Research monographs (combinatorics) |

68-02 | Research monographs (computer science) |