Integers in number systems with positive and negative quadratic Pisot base

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F14%3A00208925" target="_blank" >RIV/68407700:21340/14:00208925 - isvavai.cz</a>
Alternative codes found
RIV/60461373:22340/14:43897758
Result on the web
<a href="http://dx.doi.org/10.1051/ita/2014013" target="_blank" >http://dx.doi.org/10.1051/ita/2014013</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1051/ita/2014013" target="_blank" >10.1051/ita/2014013</a>

Result language
angličtina
Original language name
Integers in number systems with positive and negative quadratic Pisot base
Original language description
We consider numeration systems with base beta and -beta for quadratic Pisot numbers and focus on comparing the combinatorial structure of the sets Z_beta and Z_(-beta) of numbers with integer expansion in base beta, resp. -beta. Our main result is the comparison of languages of innite words u_beta and u_(-beta) coding the ordering of distances between consecutive beta- and (-beta)-integers. It turns out that for a class of roots of x2 - mx - m, the languages coincide, while for other quadratic Pisot numbers the language of u_beta can be identied only with the language of a morphic image of u_(-beta). We also study the group structure of (-beta)-integers.
Czech name
—
Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
IN - Informatics
OECD FORD branch
—

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

Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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