论文标题
Bertrand Numeration Systems的完整表征
A full characterization of Bertrand numeration systems
论文作者
论文摘要
在所有位置数字系统中，经过广泛研究的Bertrand计算系统是由简单标准根据其数值语言定义的。 1989年，Bertrand-Mathis通过在实际基础$β$中的代表来表征它们。但是，给定的条件并不是必需的。因此，本文的目的是对Bertrand-Mathis的结果进行更正。当$β$是帕里号时，主要差异是出现的，在这种情况下，两个相关的Bertrand计算系统。在此过程中，我们定义了一个非典型的$β$ shift，并类似地研究其特性与通常的规范。
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 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 are derived two associated Bertrand numeration systems. Along the way, we define a non-canonical $β$-shift and study its properties analogously to those of the usual canonical one.
