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.

We study some arithmetical and combinatorial properties of β-integers for β being the larger root of the equation x 2 =mx-n,m,n,mn+23. We determine with the accuracy of ± 1 the maximal number of β-fractional positions, which may arise as a result of addition of two β-integers. For the infinite word u β coding distances between the consecutive β-integers, we determine precisely also the balance. The word u β is the only fixed point of the morphism A A m-1 B and B A m-n-1 B. In the case n=1, the corresponding infinite word u β is sturmian, and, therefore, 1-balanced. On the simplest non-sturmian example with n 2, we illustrate how closely the balance and the arithmetical properties of β-integers are related.

DOI : https://doi.org/10.1051/ita:2007025
Classification : 68R15,  11A63
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/}
}
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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