Group of continuous transformations of real interval preserving tails of G₂-representation of numbers

In the paper, we consider a two-symbol system of encoding for real numbers with two bases having different signs g₀ < 1 and g₁ = g₀ − 1. Transformations (bijections of the set to itself) of interval [0, g₀] preserving tails of this representation of numbers are studied. We prove constructivel...

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Veröffentlicht in:Algebra and Discrete Mathematics
Datum:2020
Hauptverfasser: Pratsiovytyi, M.V., Lysenko, I.M., Maslova, Yu.P.
Format: Artikel
Sprache:Englisch
Veröffentlicht: Інститут прикладної математики і механіки НАН України 2020
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/188505
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Zitieren:Group of continuous transformations of real interval preserving tails of G₂-representation of numbers / M.V. Pratsiovytyi, I.M. Lysenko, Yu.P. Maslova // Algebra and Discrete Mathematics. — 2020. — Vol. 29, № 1. — С. 99–108. — Бібліогр.: 10 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Pratsiovytyi, M.V.
Lysenko, I.M.
Maslova, Yu.P.
author_facet Pratsiovytyi, M.V.
Lysenko, I.M.
Maslova, Yu.P.
citation_txt Group of continuous transformations of real interval preserving tails of G₂-representation of numbers / M.V. Pratsiovytyi, I.M. Lysenko, Yu.P. Maslova // Algebra and Discrete Mathematics. — 2020. — Vol. 29, № 1. — С. 99–108. — Бібліогр.: 10 назв. — англ.
collection DSpace DC
container_title Algebra and Discrete Mathematics
description In the paper, we consider a two-symbol system of encoding for real numbers with two bases having different signs g₀ < 1 and g₁ = g₀ − 1. Transformations (bijections of the set to itself) of interval [0, g₀] preserving tails of this representation of numbers are studied. We prove constructively that the set of all continuous transformations from this class with respect to composition of functions forms an infinite non-abelian group such that increasing transformations form its proper subgroup. This group is a proper subgroup of the group of transformations preserving frequencies of digits of representations of numbers.
first_indexed 2025-12-07T13:32:44Z
format Article
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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1726-3255
language English
last_indexed 2025-12-07T13:32:44Z
publishDate 2020
publisher Інститут прикладної математики і механіки НАН України
record_format dspace
spelling Pratsiovytyi, M.V.
Lysenko, I.M.
Maslova, Yu.P.
2023-03-03T16:00:12Z
2023-03-03T16:00:12Z
2020
Group of continuous transformations of real interval preserving tails of G₂-representation of numbers / M.V. Pratsiovytyi, I.M. Lysenko, Yu.P. Maslova // Algebra and Discrete Mathematics. — 2020. — Vol. 29, № 1. — С. 99–108. — Бібліогр.: 10 назв. — англ.
1726-3255
DOI:10.12958/adm1498
2010 MSC: 11H71, 26A46, 93B17
https://nasplib.isofts.kiev.ua/handle/123456789/188505
In the paper, we consider a two-symbol system of encoding for real numbers with two bases having different signs g₀ < 1 and g₁ = g₀ − 1. Transformations (bijections of the set to itself) of interval [0, g₀] preserving tails of this representation of numbers are studied. We prove constructively that the set of all continuous transformations from this class with respect to composition of functions forms an infinite non-abelian group such that increasing transformations form its proper subgroup. This group is a proper subgroup of the group of transformations preserving frequencies of digits of representations of numbers.
en
Інститут прикладної математики і механіки НАН України
Algebra and Discrete Mathematics
Group of continuous transformations of real interval preserving tails of G₂-representation of numbers
Article
published earlier
spellingShingle Group of continuous transformations of real interval preserving tails of G₂-representation of numbers
Pratsiovytyi, M.V.
Lysenko, I.M.
Maslova, Yu.P.
title Group of continuous transformations of real interval preserving tails of G₂-representation of numbers
title_full Group of continuous transformations of real interval preserving tails of G₂-representation of numbers
title_fullStr Group of continuous transformations of real interval preserving tails of G₂-representation of numbers
title_full_unstemmed Group of continuous transformations of real interval preserving tails of G₂-representation of numbers
title_short Group of continuous transformations of real interval preserving tails of G₂-representation of numbers
title_sort group of continuous transformations of real interval preserving tails of g₂-representation of numbers
url https://nasplib.isofts.kiev.ua/handle/123456789/188505
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AT lysenkoim groupofcontinuoustransformationsofrealintervalpreservingtailsofg2representationofnumbers
AT maslovayup groupofcontinuoustransformationsofrealintervalpreservingtailsofg2representationofnumbers