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arXiv · 1010.6181

Ito-Sadahiro numbers vs. Parry numbers

Zuzana Masáková·Edita Pelantová
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Abstract

We consider positional numeration system with negative base, as introduced by Ito and Sadahiro. In particular, we focus on algebraic properties of negative bases $-β$ for which the corresponding dynamical system is sofic, which happens, according to Ito and Sadahiro, if and only if the $(-β)$-expansion of $-\fracβ{β+1}$ is eventually periodic. We call such numbers $β$ Ito-Sadahiro numbers and we compare their properties with Parry numbers, occurring in the same context for Rényi positive base numeration system.

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Zuzana Masáková, Edita Pelantová. 2010-10-29. Ito-Sadahiro numbers vs. Parry numbers. https://arxiv.org/abs/1010.6181

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