Authors:Shigeki Akiyama, Horst Brunotte, and Attila Pethő
The concept of a canonical number system can be regarded as a natural generalization of decimal representations of rational
integers to elements of residue class rings of polynomial rings. Generators of canonical number systems are CNS polynomials
which are known in the linear and quadratic cases, but whose complete description is still open. In the present note reducible
CNS polynomials are treated, and the main result is the characterization of reducible cubic CNS polynomials.
Authors:Shigeki Akiyama, Tibor Borbély, Horst Brunotte, Attila Pethő, and Jörg M. Thuswaldner
Summary We are concerned with families of dynamical systems which are related to generalized radix representations. The properties of these dynamical systems lead to new results on the characterization of bases of Pisot number systems as well as canonical number systems.