Group of continuous transformations of real interval preserving tails of \(G_2\)-representation of numbers
In the paper, we consider a two-symbol system of encoding for real numbers with two bases having different signs \({g_0<1}\) and \(g_1=g_0-1\). Transformations (bijections of the set to itself) of interval \([0,g_0]\) preserving tails of this representation of numbers are studied. We prove co...
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| Дата: | 2020 |
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| Формат: | Стаття |
| Мова: | English |
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Lugansk National Taras Shevchenko University
2020
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-14982020-05-14T18:27:22Z Group of continuous transformations of real interval preserving tails of \(G_2\)-representation of numbers Pratsiovytyi, M. V. Lysenko, I. M. Maslova, Yu. P. two-symbol system of encoding for real numbers with two bases having different signs (\(G_2\)-representation), tail of representation of number, continuous transformation of interval, left and right shift operators 11H71, 26A46, 93B1 In the paper, we consider a two-symbol system of encoding for real numbers with two bases having different signs \({g_0<1}\) and \(g_1=g_0-1\). Transformations (bijections of the set to itself) of interval \([0,g_0]\) 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. Lugansk National Taras Shevchenko University 2020-05-14 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1498 10.12958/adm1498 Algebra and Discrete Mathematics; Vol 29, No 1 (2020) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1498/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/1498/623 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/1498/644 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/1498/645 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/1498/646 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/1498/647 Copyright (c) 2020 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| collection |
OJS |
| language |
English |
| topic |
two-symbol system of encoding for real numbers with two bases having different signs (\(G_2\)-representation) tail of representation of number continuous transformation of interval left and right shift operators 11H71 26A46 93B1 |
| spellingShingle |
two-symbol system of encoding for real numbers with two bases having different signs (\(G_2\)-representation) tail of representation of number continuous transformation of interval left and right shift operators 11H71 26A46 93B1 Pratsiovytyi, M. V. Lysenko, I. M. Maslova, Yu. P. Group of continuous transformations of real interval preserving tails of \(G_2\)-representation of numbers |
| topic_facet |
two-symbol system of encoding for real numbers with two bases having different signs (\(G_2\)-representation) tail of representation of number continuous transformation of interval left and right shift operators 11H71 26A46 93B1 |
| format |
Article |
| author |
Pratsiovytyi, M. V. Lysenko, I. M. Maslova, Yu. P. |
| author_facet |
Pratsiovytyi, M. V. Lysenko, I. M. Maslova, Yu. P. |
| author_sort |
Pratsiovytyi, M. V. |
| title |
Group of continuous transformations of real interval preserving tails of \(G_2\)-representation of numbers |
| title_short |
Group of continuous transformations of real interval preserving tails of \(G_2\)-representation of numbers |
| title_full |
Group of continuous transformations of real interval preserving tails of \(G_2\)-representation of numbers |
| title_fullStr |
Group of continuous transformations of real interval preserving tails of \(G_2\)-representation of numbers |
| title_full_unstemmed |
Group of continuous transformations of real interval preserving tails of \(G_2\)-representation of numbers |
| title_sort |
group of continuous transformations of real interval preserving tails of \(g_2\)-representation of numbers |
| description |
In the paper, we consider a two-symbol system of encoding for real numbers with two bases having different signs \({g_0<1}\) and \(g_1=g_0-1\). Transformations (bijections of the set to itself) of interval \([0,g_0]\) 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. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2020 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1498 |
| work_keys_str_mv |
AT pratsiovytyimv groupofcontinuoustransformationsofrealintervalpreservingtailsofg2representationofnumbers AT lysenkoim groupofcontinuoustransformationsofrealintervalpreservingtailsofg2representationofnumbers AT maslovayup groupofcontinuoustransformationsofrealintervalpreservingtailsofg2representationofnumbers |
| first_indexed |
2024-04-12T06:26:05Z |
| last_indexed |
2024-04-12T06:26:05Z |
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1796109149377921024 |