Confluent Parry numbers, their spectra, and integers in positive- and negative-base number systems
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F15%3A00221153" target="_blank" >RIV/68407700:21340/15:00221153 - isvavai.cz</a>
Alternative codes found
RIV/68407700:21240/15:00221153
Result on the web
<a href="http://dx.doi.org/10.5802/jtnb.922" target="_blank" >http://dx.doi.org/10.5802/jtnb.922</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.5802/jtnb.922" target="_blank" >10.5802/jtnb.922</a>
Alternative languages
Result language
angličtina
Original language name
Confluent Parry numbers, their spectra, and integers in positive- and negative-base number systems
Original language description
In this paper we study the expansions of real numbers in positive and negative real base as introduced by Rényi, and Ito & Sadahiro, respectively. In particular, we compare the sets ? ? + and ? -? of nonnegative ?-integers and (-?)-integers. We describeall bases (??) for which ? ? + and ? -? can be coded by infinite words which are fixed points of conjugated morphisms, and consequently have the same language. Moreover, we prove that this happens precisely for ? with another interesting property, namelythat any linear combination of non-negative powers of the base -? with coefficients in {0,1,...,[?]} is a (-?)-integer, although the corresponding sequence of digits is forbidden as a (-?)-expansion.
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/GA13-03538S" target="_blank" >GA13-03538S: Algorithms, Dynamics and Geometry of Numeration systems</a><br>
Continuities
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
J. Theor. Nombres Bordeaux
ISSN
1246-7405
e-ISSN
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Volume of the periodical
27
Issue of the periodical within the volume
3
Country of publishing house
FR - FRANCE
Number of pages
24
Pages from-to
745-768
UT code for WoS article
000369204300007
EID of the result in the Scopus database
2-s2.0-84947590631