Arithmetics in Numeration Systems with Negative Quadratic Base

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F11%3A00174144" target="_blank" >RIV/68407700:21340/11:00174144 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Arithmetics in Numeration Systems with Negative Quadratic Base
Original language description
We consider positional numeration system with negative base -betafi, as introduced by Ito and Sadahiro. In particular, we focus on arithmetical properties of such systems when fi is a quadratic Pisot number. We study a class of roots fi beta > 1 of polynomials x^2 - mx - n, m >=n >= 1, and show that in this case the set Fin(-fibeta) of finite (-betafi)-expansions is closed under addition, although it is not closed under subtraction. A particular example is fi beta =tau Fi = (1 + sqrt5)/2, the golden ratio. For such fi, we determine the exact bound on the number of fractional digits appearing in arithmetical operations. We also show that the set of (-Fibeta )-integers coincides on the positive half-line with the set of (Fi tau^2)-integers.
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
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)<br>S - Specificky vyzkum na vysokych skolach

Publication year
2011
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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