Substitution rules for aperiodic sequences of cut project type

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F00%3A04071340" target="_blank" >RIV/68407700:21340/00:04071340 - 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
Substitution rules for aperiodic sequences of cut project type
Original language description
We consider one-dimensional aperiodic sequences arising from a cut-and-project scheme with quadratic unitary Pisot numbers beta. A construction of the substitution rule is described under rather general assumptions. It allows one to build a given cut-and-project sequence Sigma (beta)(Omega) starting from its arbitrary point. For a sequence with a convex acceptance window interval Omega, we prove that a substitution rule exists precisely if the boundary points of Omega are in the corresponding quadraticfield Q[beta]. Typically such a substitution has a reducible characteristic polynomial. Our main result is an algorithm for construction of such a substitution rule. Some examples are shown.
Czech name
Substituční pravidla pro aperiodické posloupnosti typu cut-and-project
Czech description
Uvažujeme jednorozměrné aperiodické posloupnosti konstruované metodou cut-and-project pomocí kvadratických Pisotových jednotek. Ukazujeme nutnou a postačující podmínku, aby takové aperiodické posloupnosti bylo možno generovat symbolicky pomocí substitučních pravidel.

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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Publication year
2000
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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