Article (Scientific journals)
Expansions in Cantor real bases
Charlier, Emilie; Cisternino, Célia
2021In Monatshefte für Mathematik, 195, p. 585–610
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Keywords :
numeration; Cantor base; real base; shift; Parry
Abstract :
[en] We introduce and study series expansions of real numbers with an arbitrary Cantor real base. In doing so, we generalize both representations of real numbers in real bases and through Cantor series. We show fundamental properties of these new representations, each of which extends existing results on representations in a real base. In particular, we prove a generalization of Parry's theorem characterizing sequences of nonnegative integers that are the greedy representations of some real number in the interval [0,1). We pay special attention to periodic Cantor real bases, which we call alternate bases. In this case, we show that the associated shift is sofic if and only if all quasi-greedy shifted expansions of 1 are ultimately periodic.
Disciplines :
Mathematics
Author, co-author :
Charlier, Emilie  ;  Université de Liège - ULiège > Département de mathématique > Mathématiques discrètes
Cisternino, Célia ;  Université de Liège - ULiège > Département de mathématique > Mathématiques discrètes
Language :
English
Title :
Expansions in Cantor real bases
Publication date :
2021
Journal title :
Monatshefte für Mathematik
ISSN :
0026-9255
eISSN :
1436-5081
Publisher :
Springer, Germany
Volume :
195
Pages :
585–610
Peer reviewed :
Peer Reviewed verified by ORBi
Available on ORBi :
since 25 June 2020

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