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A note on univoque self-Sturmian numbers

Published online by Cambridge University Press:  04 January 2008

Jean-Paul Allouche
Jean-Paul Allouche*
Affiliation:
CNRS, LRI, UMR 8623, Université Paris Sud, Bâtiment 490, 91405 Orsay Cedex, France; allouche@lri.fr
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Abstract

We compare two sets of (infinite) binary sequences whose suffixes satisfy extremal conditions: one occurs when studying iterations of unimodal continuous maps from the unit interval into itself, but it also characterizes univoque real numbers; the other is a disguised version of the set of characteristic Sturmian sequences. As a corollary to our study we obtain that a real number β in (1,2) is univoque and self-Sturmian if and only if the β-expansion of 1 is of the form 1v, where v is a characteristic Sturmian sequence beginning itself in 1.

Keywords

Sturmian sequencesunivoque numbersself-Sturmian numbers.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 42 , Issue 4: Fibonacci words , October 2008 , pp. 659 - 662
Copyright
© EDP Sciences, 2008

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