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
Résumé
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.