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 in is univoque and self-sturmian if and only if the -expansion of is of the form , where is a characteristic sturmian sequence beginning itself in .
Mots clés : 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},
pages = {659--662},
publisher = {EDP-Sciences},
volume = {42},
number = {4},
year = {2008},
doi = {10.1051/ita:2007058},
mrnumber = {2458699},
language = {en},
url = {http://www.numdam.org/articles/10.1051/ita:2007058/}
}
TY - JOUR AU - Allouche, Jean-Paul TI - A note on univoque self-sturmian numbers JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2008 SP - 659 EP - 662 VL - 42 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ita:2007058/ DO - 10.1051/ita:2007058 LA - en ID - ITA_2008__42_4_659_0 ER -
%0 Journal Article %A Allouche, Jean-Paul %T A note on univoque self-sturmian numbers %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2008 %P 659-662 %V 42 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ita:2007058/ %R 10.1051/ita:2007058 %G en %F 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, Tome 42 (2008) no. 4, pp. 659-662. doi : 10.1051/ita:2007058. http://www.numdam.org/articles/10.1051/ita:2007058/
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