On the negative base lazy and greedy representations

Kód výsledku v 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>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

On the negative base lazy and greedy representations

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

On the negative base lazy and greedy representations

Popis výsledku anglicky

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.

Druh

O - Ostatní výsledky

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/GA201%2F09%2F0584" target="_blank" >GA201/09/0584: Algebraické a kombinatorické aspekty aperiodických struktur</a><br>

Návaznosti

Z - Vyzkumny zamer (s odkazem do CEZ)<br>S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2012

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů