From Christoffel Words to Markoff Numbers by Christophe Reutenauer (PDF)

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In 1875, Elwin Bruno Christoffel introduced a special class of words on a binary alphabet linked to continued fractions which would go onto be known as Christoffel words. Some years later, Andrey Markoff published his famous theory, the now called Markoff theory. It characterized certain quadratic forms and certain real numbers by extremal inequalities. Both classes are constructed using certain natural numbers known as Markoff numbers and they are characterized by a certain Diophantine equality. More basically, they are constructed using certain words essentially the Christoffel words. The link between Christoffel words and the theory of Markoff was noted by Ferdinand Frobenius in 1913, but has been neglected in recent times. Motivated by this overlooked connection, this book looks to expand on the relationship between these two areas. Part 1 focuses on the classical theory of Markoff, while Part II explores the more advanced and recent results of the theory of Christoffel words.

User’s Reviews

Editorial Reviews: Review “This book is a well-written introduction to a fascinating subtopic in mathematics that should be accessible to a graduate student or a research mathematician. Most subsections are a few pages in length, easily digestible in a brief time. The proofs are concise, but with enough detail to satisfy the reader.” — Jonathan Bayless, Associate Professor and Chair of Mathematics, Husson University, MAA Reviews About the Author Christophe Reutenauer, Professor of Mathematics, Universite du Quebec a MontrealChristophe Reutenauer was educated at the Universite Paris in 1977 before going on to complete his doctorate thesis at the same institution in 1980. He was a former researcher at CNRS (Centre National de la Recherche Scientifique) in Paris and LITP (Laboratoire d’Informatique Theorique et de Programmation) from 1976 to 1990.Reutenauer has, from 1985, been a professor at UQAM (Universite du Quebec a Montreal), 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 Saarbrucken, 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.

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