Real numbers having ultimately periodic representations in abstract numeration systems
<|reference_start|>Real numbers having ultimately periodic representations in abstract numeration systems: 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".<|reference_end|>
@article{lecomte2002real,
    title={Real numbers having ultimately periodic representations in abstract
  numeration systems},
    author={P. Lecomte, M. Rigo},
    journal={arXiv preprint arXiv:cs/0212018},
    year={2002},
    archivePrefix={arXiv},
    eprint={cs/0212018},
    primaryClass={cs.CC cs.CL}
}