Discriminant equations are an important class of Diophantine equations with close ties to
algebraic number theory, Diophantine approximation and Diophantine geometry. This book …

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∈ …

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

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 …

Formal Languages, Automaton and Numeration Systems presents readers with a review of
research related to formal language theory, combinatorics on words or numeration systems …

The interplay between words, computability, algebra and arithmetic has now proved its
relevance and fruitfulness. Indeed, the cross-fertilization between formal logic and finite …

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 …

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 …