Integers in number systems with positive and negative quadratic Pisot base
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 48 (2014) no. 3, pp. 341-367.

We consider numeration systems with base β and - β, for quadratic Pisot numbers β and focus on comparing the combinatorial structure of the sets Zβ and Z- β of numbers with integer expansion in base β, resp. - β. Our main result is the comparison of languages of infinite words uβ and u- β coding the ordering of distances between consecutive β- and (- β)-integers. It turns out that for a class of roots β of x2 - mx - m, the languages coincide, while for other quadratic Pisot numbers the language of uβ can be identified only with the language of a morphic image of u- β. We also study the group structure of (- β)-integers.

DOI : https://doi.org/10.1051/ita/2014013
Classification : 11K16,  68R15
Mots clés : quadratic Pisot numbers, beta-integers, negative base
@article{ITA_2014__48_3_341_0,
     author = {Mas\'akov\'a, Z. and V\'avra, T.},
     title = {Integers in number systems with positive and negative quadratic Pisot base},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {341--367},
     publisher = {EDP-Sciences},
     volume = {48},
     number = {3},
     year = {2014},
     doi = {10.1051/ita/2014013},
     mrnumber = {3302492},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ita/2014013/}
}
Masáková, Z.; Vávra, T. Integers in number systems with positive and negative quadratic Pisot base. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 48 (2014) no. 3, pp. 341-367. doi : 10.1051/ita/2014013. http://www.numdam.org/articles/10.1051/ita/2014013/

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