On the structure of (− β)-integers
W Steiner - RAIRO-Theoretical Informatics and Applications, 2012 - cambridge.org
On the structure of (-)-integers Page 1 RAIRO-Theor. Inf. Appl. 46 (2012) 181–200 Available
online at: DOI: 10.1051/ita/2011115 www.rairo-ita.org ON THE STRUCTURE OF (−β)-INTEGERS …
online at: DOI: 10.1051/ita/2011115 www.rairo-ita.org ON THE STRUCTURE OF (−β)-INTEGERS …
Noncanonical number systems in the integers
C Van De Woestijne - Journal of number theory, 2008 - Elsevier
The well-known binary and decimal representations of the integers, and other similar
number systems, admit many generalisations. Here, we investigate whether still every …
number systems, admit many generalisations. Here, we investigate whether still every …
G-Representation of Real Numbers and some of its Applications
MV Pratsiovytyi, IM Lysenko, YP Maslova… - Journal of Mathematical …, 2023 - Springer
We study a two-symbol numeral system with two bases with different signs g 0= 1 2 and g 1=-
1 2, which is an analog of the binary and nega-binary numeral systems. We prove that the …
1 2, which is an analog of the binary and nega-binary numeral systems. We prove that the …
On the number of optimal base 2 representations of integers
PJ Grabner, C Heuberger - Designs, Codes and Cryptography, 2006 - Springer
We study representations of integers n in binary expansions using the digits 0,±1. We
analyze the average number of such representations of minimal “weight”(= number of non …
analyze the average number of such representations of minimal “weight”(= number of non …
Number representation using generalized (− β)-transformation
D Dombek, Z Masáková, E Pelantová - Theoretical Computer Science, 2011 - Elsevier
We study non-standard number systems with negative base− β. Instead of the Ito–Sadahiro
definition, based on the transformation T− β of the interval [− ββ+ 1, 1β+ 1) into itself, we …
definition, based on the transformation T− β of the interval [− ββ+ 1, 1β+ 1) into itself, we …
Substitutive number systems
P Surer - International Journal of Number Theory, 2020 - World Scientific
In this paper, we associate a primitive substitution with a family of non-integer positional
number systems with respect to the same base but with different sets of digits. In this way, we …
number systems with respect to the same base but with different sets of digits. In this way, we …
[HTML][HTML] A quasi-ergodic approach to non-integer base expansions
V Komornik, P Loreti, M Pedicini - Journal of Number Theory, 2024 - Elsevier
P. Erdős et al. proved in 1990 that every nontrivial number has a continuum of expansions
on two-letter alphabets in every base smaller than the Golden ratio, and that this property …
on two-letter alphabets in every base smaller than the Golden ratio, and that this property …
[PDF][PDF] A Functional Conversion from Decimal to Base b Numbers
H Kettani - Proceedings of the 3rd Hawaii International …, 2004 - researchgate.net
We consider the problem of converting a decimal number to a base b number. We present a
conversion function that relates each digit in the base b system to the decimal value that is …
conversion function that relates each digit in the base b system to the decimal value that is …
Variants of Base 3 over 2
M Borodin, H Han, K Ji, T Khovanova, A Peng… - arXiv preprint arXiv …, 2019 - arxiv.org
We discuss two different systems of number representations that both can be called'base
3/2'. We explain how they are connected. Unlike classical fractional extension, these two …
3/2'. We explain how they are connected. Unlike classical fractional extension, these two …
[PDF][PDF] On the decimal expansion of algebraic numbers
B Adamczewski, Y Bugeaud - Fiz. Mat. Fak. Moksl. Semin. Darb, 2005 - irma.math.unistra.fr
ON THE DECIMAL EXPANSION OF ALGEBRAIC NUMBERS 1. Introduction Page 1 Fizikos ir
matematikos fakulteto Seminaro darbai, Šiauliuuniversitetas , 8, 2005, 5–13 ON THE …
matematikos fakulteto Seminaro darbai, Šiauliuuniversitetas , 8, 2005, 5–13 ON THE …