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Abstract
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.
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.
Canonical number systems in imaginary quadratic fields Acta Math. Acad. Sci. Hungar. 37 159 – 164 10.1007/BF01904880 . [10] Kátai
. , H usnine , S. M. and A hmad , S. , On existence of canonical number system in certain classes of pure algebraic number fields , J. Prime Research in Mathematics , 7 ( 2011 ), 19 – 24 . [11
