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Alternate Base Numeration Systems

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Combinatorics on Words (WORDS 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13899))

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Abstract

Alternate base numeration systems generalize real base numeration systems as defined by Renyi. Real numbers are represented using a finite number of bases periodically. Such systems naturally appear when considering linear numeration systems without a dominant root. As it happens, many classical results generalize to these numeration systems with multiple bases but some don’t. This is a survey of the work done so far concerning combinatorial, algebraic and dynamical aspects. This study has been led in collaboration with several co-authors : Célia Cisternino, Karma Dajani, Savinien Kreczman, Zuzana Masáková and Edita Pelantová.

FNRS grant J.0034.22.

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Authors and Affiliations

  1. Department of Mathematics, University of Liège, Liège, Belgium

    Émilie Charlier

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  1. Émilie Charlier
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Correspondence to Émilie Charlier .

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Editors and Affiliations

  1. Aix-Marseille University, Marseille, France

    Anna Frid

  2. Loughborough University, Loughborough, UK

    Robert Mercaş

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Charlier, É. (2023). Alternate Base Numeration Systems. In: Frid, A., Mercaş, R. (eds) Combinatorics on Words. WORDS 2023. Lecture Notes in Computer Science, vol 13899. Springer, Cham. https://doi.org/10.1007/978-3-031-33180-0_2

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  • DOI: https://doi.org/10.1007/978-3-031-33180-0_2

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-031-33180-0

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