A full characterization of Bertrand numeration systems
Combinatorics
2022-02-11 v1
Abstract
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 . However, the given condition turns to be not necessary. Hence, the goal of this paper is to provide a correction of Bertrand-Mathis' result. The main difference arises when is a Parry number, in which case are derived two associated Bertrand numeration systems. Along the way, we define a non-canonical -shift and study its properties analogously to those of the usual canonical one.
Keywords
Cite
@article{arxiv.2202.04938,
title = {A full characterization of Bertrand numeration systems},
author = {Émilie Charlier and Célia Cisternino and Manon Stipulanti},
journal= {arXiv preprint arXiv:2202.04938},
year = {2022}
}