Non-canonical Bertrand numeration systems

Date/heure
15 décembre 2022
14:00 - 15:00

Oratrice ou orateur
Emilie Charlier (université de Liège)

Catégorie d'évènement
Séminaire de Théorie des Nombres de Nancy-Metz

Among all positional numeration systems, the widely studied Bertrand numeration systems are defined by a simple criterion in terms of their numeration languages. In 1989, Bertrand-Mathis characterized them via representations in a real base $\beta$. However, the given condition turns out to be not necessary. In this talk, I will present a correction of Bertrand-Mathis’ result. The main difference arises when $\beta$ is a simple Parry number, in which case two associated Bertrand numeration systems are derived. Along the way, we define a non-canonical $\beta$-shift and study its properties analogously to those of the usual canonical one.