On a Class of Lyndon Words Extending Christoffel Words and Related to a Multidimensional Continued Fraction Algorithm
Guy Melançon
Labri
Université de Bordeaux
351, cours de la Libération
33405 Talence
France
Christophe Reutenauer
Département de Mathématiques
UQAM
Case Postale 8888, Succ. Centre-ville
Montréal, Québec H3C 3P8
Canada
Abstract:
We define a class of Lyndon words, called Christoffel-Lyndon words. We
show that they are in bijection with n-tuples of relatively prime
natural numbers. We give a geometrical interpretation of these words.
They are linked to an algorithm of Euclidean type. It admits an
extension to n-tuples of real numbers; we show that if the algorithm is
periodic, then these real numbers are algebraic of degree at most n and
that the associated multidimensional continued fraction converges to
these numbers.
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Received March 26 2013;
revised version received November 15 2013.
Published in Journal of Integer Sequences, November 17 2013.
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