 
Summary: Symmetric shift radix systems and finite
expansions
S. Akiyama and K. Scheicher
Abstract
Shift radix systems provide a unified notation to study several
important types of number systems. However, the classification of
such systems is already hard in two dimensions. In this paper, we
consider a symmetric version of this concept which turns out to be
easier: the set of such number systems with finite expansions can be
completely classified in dimension two.
1 Introduction
Shift radix systems, defined in [4], provide a unified notation for canonical
number systems (for short CNS) as well as expansions. Both concepts are
generalisations of the wellknown bary expansions of integers.
Let d 1 be an integer and r = (r1, . . . , rd) Rd
. With r we associate a
mapping ~r : Zd
Zd
in the following way: if z = (z1, . . . , zd) Zd
then
