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From Christoffel Words to Markoff Numbers$
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Christophe Reutenauer

Print publication date: 2018

Print ISBN-13: 9780198827542

Published to Oxford Scholarship Online: January 2019

DOI: 10.1093/oso/9780198827542.001.0001

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(p.69) 10 Numerology
From Christoffel Words to Markoff Numbers

Christophe Reutenauer

Oxford University Press

This chapter gives several examples, which may help the reader to work in concrete terms with Markoff numbers, Christoffel words, Markoff constants, and quadratic forms. In particular the thirteen Markoff numbers <1000 are given, together with the associated mathematical objects considered before in the book:Markoff constants, Christoffel words, the associated matrices by the representation of Chapter 3, theMarkoff quadratic numbers whose expansion is given by the Christoffel word, the Markoff quadratic forms. Some results of Frobenius, Aigner, andClemens are given. In particular thematrix associated with a Christoffel word may be computed directly from its Markoff triple.

Keywords:   Markoff constants, thirteen examples, Christoffel words, golden ratio, Frobenius congruences, continuant polynomials,Markoff quadratic forms

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