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 …

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∈ …

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 …

Substitutions are combinatorial objects (one replaces a letter by a word) which produce
sequences by iteration. They occur in many mathematical fields, roughly as soon as a …

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 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 …

Let T be a tile of a self-affine lattice tiling. We give an algorithm that allows to determine all
neighbours of T in the tiling. This can be used to characterize the sets VL of points, where T …

Number systems in Pisot number base are discussed in relation to arithmetic construction of
quasi-crystal model. One of the most important ideas is to introduce a 'dual tiling'of this …

Shift radix systems form a collection of dynamical systems depending on a parameter r
which varies in the d-dimensional real vector space. They generalize well-known …