A note on univoque self-Sturmian numbers

Details A note on univoque self-Sturmian numbers A note on univoque self-Sturmian numbers

2006-12-28

arxiv.org/abs/math/0612816v1

RAIRO Info. Th\'eor. Appl. 42 (2008) 659-662

Mathematics

Number Theory

5 pages

Scientific paper

We compare two sets of (infinite) binary sequences whose suffixes satisfy extremal conditions: one occurs when studying iterations of a unimodal continuous map from the unit interval into itself, but it also characterizes univoque real numbers; the other is an equivalent definition 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.

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