Ito-Sadahiro numbers vs. Parry numbers

Details Ito-Sadahiro numbers vs. Parry numbers Ito-Sadahiro numbers vs. Parry numbers

2010-10-29

arxiv.org/abs/1010.6181v1

Mathematics

Number Theory

10 pages

Scientific paper

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

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