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.
- ISBN10 0198827547
- ISBN13 9780198827542
- Publish Date 20 November 2018
- Publish Status Active
- Publish Country GB
- Imprint Oxford University Press
- Format Hardcover
- Pages 170
- Language English