ε-Shift Radix Systems and radix representations with shifted digit sets

About the article

Abstract

Let ε∈[0,1), r∈d and define the mapping τr,ε: d → d by

τr,ε(z) = (z1,…,zd-1,−⌊rz+ε⌋)    (z=(z0,…,zd-1)).

If for each a∈d there is a k∈ such that the k-th iterate of τr,ε satisfies τkr,ε(a) = 0 we call τr,ε an ε-shift radix system. In the present paper we unify classical shift radix systems (ε=0) and symmetric shift radix systems (ε=½), which have already been studied in several papers and analyse the relation of ε-shift radix systems to β-expansions and canonical number systems with shifted digit sets. At the end we will state several characterisation results for the two dimensional case.

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Publicationes Mathematicae Debrecen
Austrian Science Foundation (FWF)
National Research Network (NFN) S9600
Foundation "Aktion Österreich-Ungarn"