Real numbers having ultimately periodic representations in abstract numeration systems

Details Real numbers having ultimately periodic representations in abstract numeration systems Real numbers having ultimately periodic representations in abstract numeration systems

2002-12-10

arxiv.org/abs/cs/0212018v1

Computer Science

Computational Complexity

22 pages, 10 figures

Scientific paper

Using a genealogically ordered infinite regular language, we know how to represent an interval of R. Numbers having an ultimately periodic representation play a special role in classical numeration systems. The aim of this paper is to characterize the numbers having an ultimately periodic representation in generalized systems built on a regular language. The syntactical properties of these words are also investigated. Finally, we show the equivalence of the classical "theta"-expansions with our generalized representations in some special case related to a Pisot number "theta".

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