Dumont-Thomas Complement Numeration Systems for Z
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F24%3A00379531" target="_blank" >RIV/68407700:21340/24:00379531 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.5281/zenodo.14340125" target="_blank" >https://doi.org/10.5281/zenodo.14340125</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.5281/zenodo.14340125" target="_blank" >10.5281/zenodo.14340125</a>
Alternative languages
Result language
angličtina
Original language name
Dumont-Thomas Complement Numeration Systems for Z
Original language description
We extend the well-known Dumont-Thomas numeration systems to Z using an approach inspired by the two’s complement numeration system. Integers in Z are canonically represented by a finite word (starting with 0 when nonnegative and with 1 when negative). The systems are based on two-sided periodic points of substitutions as opposed to the right-sided fixed points. For every periodic point of a substitution, we construct an automaton which returns the letter at position n element Z of the periodic point when fed with the representation of n in the corresponding numeration system. The numeration system naturally extends to Zd. We give an equivalent characterization of the numeration system in terms of a total order on a regular language. Lastly, using particular periodic points, we recover the well-known two’s complement numeration system and the Fibonacci analogue of the two’s complement numeration system.
Czech name
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Czech description
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Classification
Type
J<sub>SC</sub> - Article in a specialist periodical, which is included in the SCOPUS database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
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Continuities
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Integers: Electronic Journal of Combinatorial Number Theory
ISSN
1553-1732
e-ISSN
1553-1732
Volume of the periodical
24
Issue of the periodical within the volume
A112
Country of publishing house
US - UNITED STATES
Number of pages
27
Pages from-to
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UT code for WoS article
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EID of the result in the Scopus database
2-s2.0-86000505543