Number representation using generalized (-β)-transformation

2011/02/15 by Daniel Dombek, Zuzana Masáková, Dombek, Daniel +3
Computer Science · Mathematics · #Algorithms and Data Compression #Cellular Automata and Applications #Computational Physics and Python Applications #cs.DM #math.NT

paper · pdf · doi:10.48550/arxiv.1102.3079

22 pages

arxiv created 2011/02/15 · arxiv updated 2011/02/16

Abstract

We study non-standard number systems with negative base -β. Instead of the Ito-Sadahiro definition, based on the transformation T_-β of the interval [-\fracββ+1,(1)/(β+1)) into itself, we suggest a generalization using an interval [l,l+1) with l∈(-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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