Lazy representations, substitutions and tilings associated with complex Pisot numbers

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F13%3A00207986" target="_blank" >RIV/68407700:21340/13:00207986 - 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

Lazy representations, substitutions and tilings associated with complex Pisot numbers

Popis výsledku v původním jazyce

For a complex Pisot number beta and a finite set of integer digits A, we consider the subset X^A(beta) of the set Z[beta]. Here, a complex Pisot number is a non-real algebraic integer such that |beta|>1 and all its Galois conjugates except its complex conjugate are inside the unit circle. We show how to generate this subset by a substitution on finitely many letters such that each point is generated exactly once, using so-called lazy representations. For a sufficiently large alphabet A this subset is Delone, and we then assign a tiling of the complex plane to the substitution. With the help of this tiling, we define expansions of arbitary complex numbers in our numeration system. Parts of the results are true for a larger family of beta, namely all algebraic numbers having no Galois conjugates on the unit circle.

Název v anglickém jazyce

Lazy representations, substitutions and tilings associated with complex Pisot numbers

Popis výsledku anglicky

For a complex Pisot number beta and a finite set of integer digits A, we consider the subset X^A(beta) of the set Z[beta]. Here, a complex Pisot number is a non-real algebraic integer such that |beta|>1 and all its Galois conjugates except its complex conjugate are inside the unit circle. We show how to generate this subset by a substitution on finitely many letters such that each point is generated exactly once, using so-called lazy representations. For a sufficiently large alphabet A this subset is Delone, and we then assign a tiling of the complex plane to the substitution. With the help of this tiling, we define expansions of arbitary complex numbers in our numeration system. Parts of the results are true for a larger family of beta, namely all algebraic numbers having no Galois conjugates on the unit circle.

Druh

O - Ostatní výsledky

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

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

Rok uplatnění

2013

Kód důvěrnosti údajů

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