Geodesic
A note on univoque self-sturmian numbers
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 42 (2008) no. 4, pp. 659-662

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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.

DOI : 10.1051/ita:2007058
Classification : 11A63, 68R15
Keywords: sturmian sequences, univoque numbers, self-sturmian numbers 
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     title = {A note on univoque self-sturmian numbers},
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Allouche, Jean-Paul. A note on univoque self-sturmian numbers. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 42 (2008) no. 4, pp. 659-662. doi: 10.1051/ita:2007058

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