Characterization of quadratic ε−CNS polynomials

Abstract

In this paper, we give characterization of quadratic ε-canonical number system (ε−CNS) polynomials for all values $\epsilon \in [0,1)$. Our characterization provides a unified view of the well-known characterizations of the classical quadratic CNS polynomials ($\epsilon =0$) and quadratic SCNS polynomials ($\epsilon =1/2$). This result is a consequence of our new characterization results of ε-shift radix systems (ε−SRS) in the two-dimensional case and their relation to quadratic ε−CNS polynomials.