A note on univoque self-sturmian numbers

Allouche, Jean-Paul

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 42 (2008) no. 4, pp. 659-662.

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 $\beta$ in $(1,2)$ is univoque and self-sturmian if and only if the $\beta$-expansion of $1$ is of the form $1v$, where $v$ is a characteristic sturmian sequence beginning itself in $1$.

Classification : 11A63, 68R15
Mots clés : sturmian sequences, univoque numbers, self-sturmian numbers

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