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 …

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 …

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

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 …

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 study properties of the fundamental domain [Fscr] β of number systems,
which are defined in rings of integers of number fields. First we construct addition automata …

This paper studies closed 3-manifolds which are the attractors of a system of finitely many
affine contractions that tile R 3. Such attractors are called self-affine tiles. Effective …

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 …

Let T= T (A, D) be a self-affine tile in\reals^ n defined by an integral expanding matrix A and
a digit set D. In connection with canonical number systems, we study connectedness of T …