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A full characterization of Bertrand numeration systems
Charlier, Emilie
2022
 

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Keywords :
Numeration system; Integer; Real number; Beta-shift
Abstract :
[en] 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 β. However, the given condition turns out to be not necessary. Hence, the goal of this paper is to provide a correction of Bertrand-Mathis' result. The main difference arises when β is a Parry number, in which case two associated Bertrand numeration systems are derived. Along the way, we define a non-canonical β-shift and study its properties analogously to those of the usual canonical one.
Disciplines :
Mathematics
Author, co-author :
Charlier, Emilie  ;  Université de Liège - ULiège > Mathematics
Language :
English
Title :
A full characterization of Bertrand numeration systems
Publication date :
March 2022
Event name :
Séminaire du GT de combinatoire et interactions du LaBRI
Event date :
21 mars 2022
Audience :
International
Available on ORBi :
since 21 March 2022

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