Finiteness property in Cantor real numeration systems

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Finiteness property in Cantor real numeration systems

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Finiteness property in Cantor real numeration systems

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2025

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas

ISSN

1578-7303

e-ISSN

1579-1505

Svazek periodika

119

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

25

Strana od-do

—

Kód UT WoS článku

001394216600001

EID výsledku v databázi Scopus

2-s2.0-86000260052