A note on univoque self-sturmian numbers
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 42 (2008) no. 4, p. 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 $\left(1,2\right)$ 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 $1$.

DOI : https://doi.org/10.1051/ita:2007058
Classification:  11A63,  68R15
Keywords: sturmian sequences, univoque numbers, self-sturmian numbers
@article{ITA_2008__42_4_659_0,
author = {Allouche, Jean-Paul},
title = {A note on univoque self-sturmian numbers},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
publisher = {EDP-Sciences},
volume = {42},
number = {4},
year = {2008},
pages = {659-662},
doi = {10.1051/ita:2007058},
zbl = {pre05363211},
mrnumber = {2458699},
language = {en},
url = {http://www.numdam.org/item/ITA_2008__42_4_659_0}
}

Allouche, Jean-Paul. A note on univoque self-sturmian numbers. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 42 (2008) no. 4, pp. 659-662. doi : 10.1051/ita:2007058. http://www.numdam.org/item/ITA_2008__42_4_659_0/

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