A Full Characterization of Bertrand Numeration Systems

被引：0

作者：

Charlier, Emilie ^{[1
]}

Cisternino, Celia ^{[1
]}

Stipulanti, Manon ^{[1
]}

机构：

[1] Univ Liege, Dept Math, Liege, Belgium

来源：

DEVELOPMENTS IN LANGUAGE THEORY (DLT 2022) | 2022年 / 13257卷

关键词：

Numeration systems; Bertrand condition; Real bases expansion; Dominant root; Parry numbers; Subshifts; PARRY; BASE;

D O I：

10.1007/978-3-031-05578-2_8

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

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. Hence, the goal of this paper is to provide a correction of Bertrand-Mathis' result. The main difference arises when beta is a 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.

引用

页码：102 / 114

页数：13

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