Purely periodic expansions in systems with negative base

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F13%3A00192718" target="_blank" >RIV/68407700:21340/13:00192718 - isvavai.cz</a>
Result on the web
<a href="http://www.springerlink.com/content/e3488335063132k1/" target="_blank" >http://www.springerlink.com/content/e3488335063132k1/</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10474-012-0261-0" target="_blank" >10.1007/s10474-012-0261-0</a>

Result language
angličtina
Original language name
Purely periodic expansions in systems with negative base
Original language description
We study the question of pure periodicity of expansions in the negative base numeration system. In analogy of Akiyama's result for positive Pisot unit base $beta$, we find a sufficient condition so that there exist an interval $J$ containing the origin such that the $(-beta)$-expansion of every rational number from $J$ is purely periodic. We focus on the case of quadratic bases and demonstrate the following difference between the negative and positive bases: It is known that the finiteness property (${rm Fin}(beta)=Z[beta]$) is not only sufficient, but also necessary in the case of positive quadratic and cubic bases. We show that ${rm Fin}(-beta)=Z[beta]$ is not necessary in the case of negative bases.
Czech name
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Czech description
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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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Project
<a href="/en/project/GA201%2F09%2F0584" target="_blank" >GA201/09/0584: Algebraic and combinatorial aspects of aperiodic structures</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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