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Expansions in multiple bases over general alphabets

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Abstract

Expansions in non-integer bases have been extensively investigated since a pioneering work of Rényi. We introduce a more general framework of alphabet-base systems that also includes Pedicini’s general alphabets and the multiple-base expansions of Neunhäuserer and Li. We extend the Parry type lexicographic theory to this setup, and we improve and generalize various former results on unique expansions.

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Authors and Affiliations

  1. College of Mathematics and Statistics, Shenzhen University, Shenzhen, 518060, People’s Republic of China

    V. Komornik, J. Lu & Y. Zou

  2. Département de mathématique, Université de Strasbourg, 7 rue René Descartes, Strasbourg Cedex , 67084, France

    V. Komornik

Authors
  1. V. Komornik
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  2. J. Lu
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  3. Y. Zou
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Corresponding author

Correspondence to Y. Zou.

Additional information

This work was supported by the National Natural Science Foundation of China (NSFC) #11871348 and #61972265, by the Natural Science Foundation of Guangdong Province of China #2020B1515310008, by the Project of Educational Commission of Guangdong Province of China #2019KZDZX1007, by Shenzhen Basis Research Project #JCYJ20180305125521534, and by the grants CAPES: No. 88881.520205/2020-01 and MATH AMSUD: 21-MATH-03.

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Komornik, V., Lu, J. & Zou, Y. Expansions in multiple bases over general alphabets. Acta Math. Hungar. 166, 481–506 (2022). https://doi.org/10.1007/s10474-022-01231-4

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  • DOI: https://doi.org/10.1007/s10474-022-01231-4

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