On the negative base lazy and greedy representations

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F12%3A00198419" target="_blank" >RIV/68407700:21340/12:00198419 - 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
On the negative base lazy and greedy representations
Original language description
We consider positional numeration systems with negative real base minus-betafi, where betafi > 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 (minus-betafi)-representation with respect to the alternate order. We also show that both extremal representations can be obtained using the positive base beta^fi2 and a non-integer alphabet. This enables us to characterize digit sequences admissible as greedy and lazy (minus-betafi)-representation. Such a characterization allows us to study the set of uniquely representable numbers. In case that fiis the golden ratio, we give the characterization of digit sequences admissible as greedy and lazy (minus-betafi)-representation using a set of forbidden strings.
Czech name
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Czech description
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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
Z - Vyzkumny zamer (s odkazem do CEZ)<br>S - Specificky vyzkum na vysokych skolach

Publication year
2012
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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