We study the complexity of the infinite word associated with the Rényi expansion of in an irrational base . When is the golden ratio, this is the well known Fibonacci word, which is sturmian, and of complexity . For such that is finite we provide a simple description of the structure of special factors of the word . When we show that . In the cases when or we show that the first difference of the complexity function takes value in for every , and consequently we determine the complexity of . We show that is an Arnoux-Rauzy sequence if and only if . On the example of , solution of , we illustrate that the structure of special factors is more complicated for infinite eventually periodic. The complexity for this word is equal to .
Mots clés : beta-expansions, complexity of infinite words
@article{ITA_2004__38_2_163_0, author = {Frougny, Christiane and Mas\'akov\'a, Zuzana and Pelantov\'a, Edita}, title = {Complexity of infinite words associated with beta-expansions}, journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications}, pages = {163--185}, publisher = {EDP-Sciences}, volume = {38}, number = {2}, year = {2004}, doi = {10.1051/ita:2004009}, mrnumber = {2060775}, zbl = {1104.11013}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/ita:2004009/} }
TY - JOUR AU - Frougny, Christiane AU - Masáková, Zuzana AU - Pelantová, Edita TI - Complexity of infinite words associated with beta-expansions JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2004 SP - 163 EP - 185 VL - 38 IS - 2 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ita:2004009/ DO - 10.1051/ita:2004009 LA - en ID - ITA_2004__38_2_163_0 ER -
%0 Journal Article %A Frougny, Christiane %A Masáková, Zuzana %A Pelantová, Edita %T Complexity of infinite words associated with beta-expansions %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2004 %P 163-185 %V 38 %N 2 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ita:2004009/ %R 10.1051/ita:2004009 %G en %F ITA_2004__38_2_163_0
Frougny, Christiane; Masáková, Zuzana; Pelantová, Edita. Complexity of infinite words associated with beta-expansions. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 38 (2004) no. 2, pp. 163-185. doi : 10.1051/ita:2004009. http://archive.numdam.org/articles/10.1051/ita:2004009/
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