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From Christoffel Words to Markoff Numbers
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From Christoffel Words to Markoff Numbers

Christophe Reutenauer

Abstract

Christoffel introduced in 1875 a special class of words on a binary alphabet, linked to continued fractions. Some years laterMarkoff published his famous theory, called nowMarkoff theory. It characterizes certain quadratic forms, and certain real numbers by extremal inequalities. Both classes are constructed by using certain natural numbers, calledMarkoff numbers; they are characterized by a certain diophantine equality. More basically, they are constructed using certain words, essentially the Christoffel words. The link between Christoffelwords and the theory ofMarkoffwas noted by Frobenius.M ... More

Keywords: combinatorics on words, continued fractions, diophantine approximation, quadratic forms, palindromes

Bibliographic Information

Print publication date: 2018 Print ISBN-13: 9780198827542
Published to Oxford Scholarship Online: January 2019 DOI:10.1093/oso/9780198827542.001.0001

Authors

Affiliations are at time of print publication.

Christophe Reutenauer, author
Professor of Mathematics, Université du Québec à Montréal