Addition in Dumont-Thomas Numeration Systems in Theory and Practice
<|reference_start|>Addition in Dumont-Thomas Numeration Systems in Theory and Practice: Given a fixpoint of a substitution, the associated Dumont-Thomas numeration system provides a convenient immediate way to describe the fixpoint as an automatic sequence. In order to study first-order properties of these fixpoints using B\"uchi-Bruy\`ere characterization, it is necessary for the numeration system to be addable. This means that its addition relation must be computable by a finite automaton. Dumont-Thomas numeration systems can be regarded as an extension of positional numeration systems with states where the greediness is state-dependent. We introduce sequence automata as a tool to extend the results of Bruy\`ere-Hansel and Frougny-Solomyak on the regularity of the addition of Bertrand numeration systems to the case of Dumont-Thomas numeration systems related to some Pisot number. We present a practical implementation of the addition compatible with the Walnut computation tool, along with some experimental results.<|reference_end|>
@article{carton2024addition,
    title={Addition in Dumont-Thomas Numeration Systems in Theory and Practice},
    author={Olivier Carton, Jean-Michel Couvreur, Martin Delacourt, Nicolas
  Ollinger},
    journal={arXiv preprint arXiv:2406.09868},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.09868},
    primaryClass={cs.FL cs.DM math.CO}
}