Lazy representations, substitutions and tilings associated with complex Pisot numbers

Result code in 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>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Lazy representations, substitutions and tilings associated with complex Pisot numbers
Original language description
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.
Czech name
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Czech description
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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
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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