Finiteness property in Cantor real numeration systems
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F25%3A00379324" target="_blank" >RIV/68407700:21340/25:00379324 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s13398-024-01695-9" target="_blank" >https://doi.org/10.1007/s13398-024-01695-9</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s13398-024-01695-9" target="_blank" >10.1007/s13398-024-01695-9</a>
Alternative languages
Result language
angličtina
Original language name
Finiteness property in Cantor real numeration systems
Original language description
We consider a numeration system which is a common generalization of the positional systems introduced by Cantor and Rényi. Number representations are obtained using a composition of βk-transformations for a given sequence of real bases B = (βk)k>=1, βk > 1. We focus on arithmetical properties of the set of numbers with finite B-expansion in case that B is an alternate base, i.e. B is a periodic sequence. We provide necessary conditions for the so-called finiteness property. We further show a sufficient condition using rewriting rules on the language of representations. The proof is constructive and provides a method for performing addition of expansions in alternate bases. Finally, we give a family of alternate bases that satisfy this sufficient condition. Our work generalizes the results of Frougny and Solomyak obtained for the case when the base B is a constant sequence.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
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Continuities
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
ISSN
1578-7303
e-ISSN
1579-1505
Volume of the periodical
119
Issue of the periodical within the volume
2
Country of publishing house
DE - GERMANY
Number of pages
25
Pages from-to
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UT code for WoS article
001394216600001
EID of the result in the Scopus database
2-s2.0-86000260052