From Christoffel Words to Markoff Numbers

@inproceedings{Reutenauer2018FromCW,
title={From Christoffel Words to Markoff Numbers},
author={Christophe Reutenauer},
year={2018}
}
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…
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