This paper surveys different constructions and properties of some multiple tilings (that is,
finite-to-one coverings) of the space that can be associated with beta-numeration and …

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 …

We are concerned with the tiling flow T associated to a substitution φ over a finite alphabet.
Our focus is on substitutions that are unimodular Pisot, ie, their matrix is unimodular and has …

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 …

An irreducible Pisot substitution defines a graph-directed iterated function system. The
invariant sets of this iterated function system are called the atomic surfaces. In this paper, a …

We are interested here in the pure discrete spectrum property for Pisot substitutions.
Traditionally, this would mean considering the pure discreteness of the unitary operator f↦→ …

This paper studies tilings and representation sapces related to the β-transformation when β
is a Pisot number (that is not supposed to be a unit). The obtained results are applied to …

The atomic surfaces of unimodular Pisot substitutions of irreducible type have been studied
by many authors. In this article, we study the atomic surfaces of Pisot substitutions of …

A substitution is a rule that replaces letters by words. A famous example is the Fibonacci
substitution defined by a↦→ ab and b↦→ a. It can be iterated to produce an infinite word: a …