Finite beta-expansions with negative bases

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F17%3A00308832" target="_blank" >RIV/68407700:21340/17:00308832 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/s10474-017-0711-9" target="_blank" >http://dx.doi.org/10.1007/s10474-017-0711-9</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10474-017-0711-9" target="_blank" >10.1007/s10474-017-0711-9</a>

Result language
angličtina
Original language name
Finite beta-expansions with negative bases
Original language description
The finiteness property is an important arithmetical property of beta-expansions. We exhibit classes of Pisot numbers $beta$ having the negative finiteness property, that is the set of finite (-beta)-expansions is equal to Z[beta^(-1)]. For a class of numbers including the Tribonacci number, we compute the maximal length of the fractional parts arising in the addition and subtraction of (-beta)-integers. We also give conditions excluding the negative finiteness property.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA13-03538S" target="_blank" >GA13-03538S: Algorithms, Dynamics and Geometry of Numeration systems</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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