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 …

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 …

Our goal is to present a unified and reasonably complete account of the various conjectures,
known as Pisot conjectures, that assert that certain dynamical systems arising from …

It is well known that real numbers with a purely periodic decimal expansion are rationals
having, when reduced, a denominator coprime with 10. The aim of this paper is to extend …

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↦→ …

The aim of this survey is to illustrate various connections that exist between word
combinatorics and arithmetic discrete geometry through the discussion of some …

For a (non-unit) Pisot number β, several collections of tiles are associated with β-
numeration. This includes an aperiodic and a periodic one made of Rauzy fractals, a …

This paper discusses the relation between three groups: the dynamical cohomology H (T) of
a substitution shift dynamical system T, the first integer Čech cohomology group H¹ (Y) of the …

In this paper, we associate a primitive substitution with a family of non-integer positional
number systems with respect to the same base but with different sets of digits. In this way, we …