Abstract:
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.
Keywords:
two-symbol system of encoding for real numbers with two bases having different signs (G2-representation), tail of representation of number, continuous transformation of interval, left and right shift operators, continuous transformation preserving tails of representations.
Citation:
M. V. Pratsiovytyi, I. M. Lysenko, Yu. P. Maslova, “Group of continuous transformations of real interval preserving tails of G2-representation of numbers”, Algebra Discrete Math., 29:1 (2020), 99–108
\Bibitem{PraLysMas20}
\by M.~V.~Pratsiovytyi, I.~M.~Lysenko, Yu.~P.~Maslova
\paper Group of continuous transformations of real interval preserving tails of $G_2$-representation of numbers
\jour Algebra Discrete Math.
\yr 2020
\vol 29
\issue 1
\pages 99--108
\mathnet{http://mi.mathnet.ru/adm742}
\crossref{https://doi.org/10.12958/adm1498}
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Linking options:
https://www.mathnet.ru/eng/adm742
https://www.mathnet.ru/eng/adm/v29/i1/p99
This publication is cited in the following 7 articles:
Mykola Pratsiovytyi, Sofiia Ratushniak, Lysenko Iryna, “Uncountable group of continuous transformations of unit segment preserving tails of Q_2-representation of numbers”, PIGC, 17:2 (2024), 133
V. Yelahin, “NEGA-QS-REPRESENTATION OF NUMBERS AND ITS CORRESPONDING TAIL SETS”, BMJ, 12:2 (2024), 80
I. Lysenko, O. Pratsiovytyi, V. Plakyda, “CONTINUOUS FUNCTIONS DEFINED IN TERMS OF A TWO-SYMBOL \MATHBFG2-REPRESENTATION WITH TWO BASES HAVING DIFFERENT SIGNS”, BMJ, 12:2 (2024), 89
M. V. Pratsiovytyi, I. M. Lysenko, Yu.P. Maslova, O. O. Trebenko, “G-Representation of Real Numbers and some of its Applications”, J Math Sci, 277:2 (2023), 298
M. Pratsiovytyi, N. Vasylenko, Ya. Goncharenko, I. Lysenko, “TWO-SYMBOL SYSTEM OF ENCODING OF NUMBERS AND DISCRETE DISTRIBUTIONS OF RANDOM VARIABLES”, BMJ, 11:2 (2023), 225
M. Pratsiovytyi, V. Drozdenko, I. Lysenko, Yu. Maslova, “INVERSOR OF DIGITS OF TWO-BASE G–REPRESENTATION OF REAL NUMBERS AND ITS STRUCTURAL FRACTALITY”, BMJ, 10:1 (2022), 100
M.V. Pratsovytyi, Ya. V. Goncharenko, I. M. Lysenko, S.P. Ratushniak, “Fractal functions of exponential type that is generated by the Q∗2-representation of argument”, Mat. Stud., 56:2 (2021), 133
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