Mathematics is notably concerned with the study of numbers and the arithmetic properties of
these numbers in relation with the syntactical properties of their representations by …

We introduce and study series expansions of real numbers with an arbitrary Cantor real
base β=(β _n) _ n ∈ N β=(β n) n∈ N, which we call β β-representations. In doing so, we …

For alternate Cantor real base numeration systems we generalize the result of Frougny and~
Solomyak on~ arithmetics on the set of numbers with finite expansion. We provide a class of …

The lazy algorithm for a real base $\beta $ is generalized to the setting of Cantor bases
$\boldsymbol {\beta}=(\beta_n) _ {n\in\mathbb {N}} $ introduced recently by Charlier and the …

Alternate base numeration systems generalize real base numeration systems as defined by
Renyi. Real numbers are represented using a finite number of bases periodically. Such …

The main object of this thesis are numeration systems, sometimes also called number
systems or numeral systems, which are different ways of representing numbers using (finite …

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 …

We answer the following question: If p and q are positive integers greater than 1 and C p is
the set of all numbers in [0, 1] which can be expressed in base p without using a nonempty …

We consider Cantor real numeration system as a frame in which every non-negative real
number has a positional representation. The system is defined using a bi-infinite sequence …

We generalize the greedy and lazy-transformations for a real base to the setting of alternate
bases, which were recently introduced by the first and second authors as a particular case of …