Three-dimensional symmetric shift radix systems

Abstract

Shift radix systems have been introduced by Akiyama et al. as a common generalization of β-expansions and canonical number systems. In the present paper we study a variant of them, so-called symmetric shift radix systems which were introduced recently by Akiyama and Scheicher. In particular, for d ∈ N and r ∈ R let (a = (a1, . . . , ad)) τr : Z d → Z, a 7→ (