From Christoffel Words to Markoff Numbers

Christophe Reutenauer was educated at École Normale Supérieure in Paris, and subsequently undertook his postgraduate studies at the Université de Paris 6 in 1977, before going on to complete his doctorate thesis at the same institution in 1980. He was a former researcher at the CNRS (Centre National de la Recherche Scientifique) in Paris, and LITP (Laboratoire d'Informatique Théorique et de Programmation) from 1976 to 1990. Reutenauer has been a professor at UQAM (Université du Québec à Montréal) since 1985, and was also a professor at the University of Strasbourg between 1999 and 2001. Since then, he has been an invited professor or researcher at several universities, including Saarbrücken, Darmstadt, Roma, Napoli, Palermo, UQAM, San Diego (UCSD), Strasbourg, Montpelier, Bordeaux, Paris-Est, Nice, and the Mittag-Leffler Institute. He was also the Canadian Research Chair for Algebra, Combinatorics and mathematical Informatics between 2001 and 2015.

• Part I The theory of Markoff 1: Basics 2: Words 3: Markoff numbers 4: The Markoff property 5: Continued fractions 6: Binary quadratic forms 7: Lagrange number 8: Words and quadratic numbers 9: Lagrange numbers less than three 10: Markoff's theorem for approximations 11: Markoff's theorem for quadratic forms 12: Numerology 13: Historical notes Part II The theory of Christoffel words 14: Palindromes and periods 15: Conjugates and factors 16: Standard words 17: Lyndon words and Christoffel words 18: Sturmian words 19: Stern-Brocot tree 20: Free group on two generators 21: The commutator subgroup SL2(Z)'

Review from previous edition For the first time in literature on the subject, this textbook treats the two aspects of Markoff's Theory simultaneously. Numerous figures throughout the book help to illustrate its points and provide proofs of discrete geometry.