Greedy and lazy representations in negative base systems

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F13%3A00199836" target="_blank" >RIV/68407700:21340/13:00199836 - 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
Greedy and lazy representations in negative base systems
Original language description
We consider positional numeration systems with negative real base -beta, where beta > 1, and study the extremal representations in these systems, called here the greedy and lazy representations. We give algorithms for determination of minimal and maximal(-beta)- representation with respect to the alternate order. We also show that both extremal representations can be obtained using the positive base beta^2 and a non-integer alphabet. This enables us to characterize digit sequences admissible as greedyand lazy (-beta)-representation. Such a characterization allows us to study the set of uniquely representable numbers. In case that is the golden ratio and the Tribonacci constant, we give the characterization of digit sequences admissible as greedy andlazy (-beta)-representation using a set of forbidden strings.
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
S - Specificky vyzkum na vysokych skolach

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

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