Number representation using generalized (-?)-transformation
Result description
We study non-standard number systems with negative base -?. Instead of the Ito-Sadahiro definition, based on the transformation of the interval [-?/(?+1),1/(?+1)) into itself, we suggest a generalization using an interval [l,l+1) with l in (-1,0]. Such numeration systems share many properties of positive base numeration introduced by Rényi, although the proofs are not always straightforward. In this paper we focus on the description of admissible digit strings and their periodicity. We address the question of the description of reference strings used in the admissibility condition. We give examples which contradict a result of Góra and show that in this aspect the negative base numeration significantly differs from the Rényi numeration.
Keywords
The result's identifiers
Result code in IS VaVaI
Result on the web
DOI - Digital Object Identifier
Alternative languages
Result language
angličtina
Original language name
Number representation using generalized (-?)-transformation
Original language description
We study non-standard number systems with negative base -?. Instead of the Ito-Sadahiro definition, based on the transformation of the interval [-?/(?+1),1/(?+1)) into itself, we suggest a generalization using an interval [l,l+1) with l in (-1,0]. Such numeration systems share many properties of positive base numeration introduced by Rényi, although the proofs are not always straightforward. In this paper we focus on the description of admissible digit strings and their periodicity. We address the question of the description of reference strings used in the admissibility condition. We give examples which contradict a result of Góra and show that in this aspect the negative base numeration significantly differs from the Rényi numeration.
Czech name
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Czech description
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Classification
Type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
GA201/09/0584: Algebraic and combinatorial aspects of aperiodic structures
Continuities
Z - Vyzkumny zamer (s odkazem do CEZ)
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2011
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Theoretical Computer Science
ISSN
0304-3975
e-ISSN
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Volume of the periodical
412
Issue of the periodical within the volume
48
Country of publishing house
GB - UNITED KINGDOM
Number of pages
13
Pages from-to
6653-6665
UT code for WoS article
000296987400003
EID of the result in the Scopus database
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Basic information
Result type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP
BA - General mathematics
Year of implementation
2011