On relationships between shift radix systems and canonical number systems

Horst Brunotte

Coauthor(s): Shigeki Akiyama, Attila Pethö, and Jörg M. Thuswaldner

Shift radix systems are intimately related to certain well-known notions of number systems like $\beta$-expansions and canonical number systems. In the talk structural relationships between shift radix systems and canonical number systems are investigated. Among other results it is shown that canonical number systems related to monic integral polynomials of degree $d \ge 2$ with large but fixed constant terms approximate the set of shift radix systems in dimension $d-1$. The main results settle two conjectures established by the authors in an earlier publication.

Partially supported by the Austrian Science Foundation (FWF), project S9610.