This collaborative volume presents recent trends arising from the fruitful interaction between
the themes of combinatorics on words, automata and formal language theory, and number …

GENERALIZED RADIX REPRESENTATIONS AND DYNAMICAL SYSTEMS. I Page 1 Acta
Math. Hungar. 108 (3) (2005), 207–238. GENERALIZED RADIX REPRESENTATIONS AND …

Let P (x)= p dx d+⋯+ p 0∈ Z [x] be such that d⩾ 1, pd= 1, p 0⩾ 2 and N={0, 1,…, p 0− 1}. We
are proving in this note a new criterion for the pair {P (x), N} to be a canonical number …

Let P (x)= xd+ pd− 1xd− 1+···+ p0 be an expanding monic polynomial with integer
coefficients. If each element of Z [x]/P (x) Z [x] has a polynomial representative with …

Canonical Number System can be considered as natural generalization of radix
representation of rational integers to algebraic integers. We determine the existence of …

Let α be a root of an irreducible quadratic polynomial x2+ Ax+ B with integer coefficients A, B
and assume that α forms a canonical number system, ie, each x∈ ℤ [α] admits a …

It is well known that each positive integer can be expressed uniquely as a sum= 0+ 1+···+
with an integral base number≥ 2,= 0 and∈{0...− 1}. This concept can be generalized in …

In this paper, we give characterization of quadratic $\varepsilon-$ canonical number system
($\varepsilon-$ CNS) polynomials for all values $\varepsilon\in\lbrack0, 1) $. Our …

In this paper, we give characterization of quadratic ε-canonical number system (ε− CNS)
polynomials for all values ε∈[0, 1). Our characterization provides a unified view of the well …

Canonical number systems can be viewed as natural generalizations of radix
representations of ordinary integers to algebraic integers. A slightly modified version of an …