Three-dimensional symmetric shift radix systems

Abstract

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 ∈ Rd let (a = (a1,...,ad)) τr: Z d → Z d, a ↦→ a2,...,ad, − r1a1 + r2a2 + · · · + rdad + 1