Number representation using generalized $(-β)$-transformation

Details Number representation using generalized $(-β)$-transformation Number representation using generalized $(-β)$-transformation

2011-02-15

arxiv.org/abs/1102.3079v1

Computer Science

Discrete Mathematics

22 pages

Scientific paper

We study non-standard number systems with negative base $-\beta$. Instead of the Ito-Sadahiro definition, based on the transformation $T_{-\beta}$ of the interval $\big[-\frac{\beta}{\beta+1},\frac{1}{\beta+1}\big)$ into itself, we suggest a generalization using an interval $[l,l+1)$ with $l\in(-1,0]$. Such generalization may eliminate certain disadvantages of the Ito-Sadahiro system. We focus on the description of admissible digit strings and their periodicity.

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