From Christoffel Words to Markoff Numbers - Christophe Reutenauer

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From Christoffel Words to Markoff Numbers

By: Christophe Reutenauer

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Hardcover | 29 November 2018

At a Glance

Hardcover
170 Pages

Dimensions(cm)
24.13 x 15.88 x 1.27

Hardcover

RRP $230.00

$169.75

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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.

Industry Reviews

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. * Ioan Tomescu, zbMath *
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 *

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