Uniting dozens of seemingly disparate results from different fields, this book combines
concepts from mathematics and computer science to present the first integrated treatment of …

Let d≥ 1 be an integer and r=(r0,..., rd− 1)∈ Rd. The shift radix system τr: Zd→ Zd is defined
by τr (z)=(z1,..., zd− 1,−⌊ rz⌋) t (z=(z0,..., zd− 1) t). τr has the finiteness property if each z∈ …

In this paper, we characterize whether the pure sextic fields with square-free integers m≢±1
(Mod 9) have power integral bases or do not; if m≡ 2, 3 (Mod 4), then have power integral …

Le but de ce survol est d'aborder définitions et propriétés concernant la numération d'un
point de vue dynamique: nous nous concentrons sur les systèmes de numération, leur …

In the present paper we give an overview of topological properties of self-affine tiles. After
reviewing some basic results on self-affine tiles and their boundary we give criteria for their …

We consider the disklikeness of the planar self-affine tile $ T $ generated by an integral
expanding matrix $ A $ and a consecutive collinear digit set ${\mathcal {D}}=\{0, v …

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 …

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 …