We prove that all algebraic bases β allow an eventually periodic representation of the elements of ℚ(β) with a finite alphabet of digits \({\cal A}\). Moreover, the classification of bases allowing that those representations have the socalled weak greedy property is given.

The decision problem whether a given pair (β, \({\cal A}\)) allows eventually periodic representations proves to be rather hard, for it is equivalent to a topological property of the attractor of an iterated function system.

中文翻译：

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塞勒姆基地的定期代表制

我们证明所有的代数基β都可以用有限的数字\（{\ cal A} \）来最终表示ℚ（β）的元素。此外，给出了允许这些表示具有所谓的弱贪婪属性的基数分类。

给定对（β，\（{\ cal A} \））是否最终允许周期性表示的决策问题被证明是相当困难的，因为它等效于迭代函数系统的吸引子的拓扑性质。