We study some arithmetical and combinatorial properties of -integers for being the larger root of the equation . We determine with the accuracy of 1 the maximal number of -fractional positions, which may arise as a result of addition of two -integers. For the infinite word coding distances between the consecutive -integers, we determine precisely also the balance. The word is the only fixed point of the morphism and . In the case , the corresponding infinite word is sturmian, and, therefore, -balanced. On the simplest non-sturmian example with 2, we illustrate how closely the balance and the arithmetical properties of -integers are related.
Mots-clés : balance property, arithmetics, beta-expansions, infinite words
@article{ITA_2007__41_3_307_0, author = {Balkov\'a, Lubom{\'\i}ra and Pelantov\'a, Edita and Turek, Ond\v{r}ej}, title = {Combinatorial and arithmetical properties of infinite words associated with non-simple quadratic {Parry} numbers}, journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications}, pages = {307--328}, publisher = {EDP-Sciences}, volume = {41}, number = {3}, year = {2007}, doi = {10.1051/ita:2007025}, mrnumber = {2354360}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/ita:2007025/} }
TY - JOUR AU - Balková, Lubomíra AU - Pelantová, Edita AU - Turek, Ondřej TI - Combinatorial and arithmetical properties of infinite words associated with non-simple quadratic Parry numbers JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2007 SP - 307 EP - 328 VL - 41 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ita:2007025/ DO - 10.1051/ita:2007025 LA - en ID - ITA_2007__41_3_307_0 ER -
%0 Journal Article %A Balková, Lubomíra %A Pelantová, Edita %A Turek, Ondřej %T Combinatorial and arithmetical properties of infinite words associated with non-simple quadratic Parry numbers %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2007 %P 307-328 %V 41 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ita:2007025/ %R 10.1051/ita:2007025 %G en %F ITA_2007__41_3_307_0
Balková, Lubomíra; Pelantová, Edita; Turek, Ondřej. Combinatorial and arithmetical properties of infinite words associated with non-simple quadratic Parry numbers. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 41 (2007) no. 3, pp. 307-328. doi : 10.1051/ita:2007025. http://archive.numdam.org/articles/10.1051/ita:2007025/
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