On generalized self-similarities of cut-and-project sets

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F21%3A00345343" target="_blank" >RIV/68407700:21340/21:00345343 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.laa.2021.05.010" target="_blank" >https://doi.org/10.1016/j.laa.2021.05.010</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.laa.2021.05.010" target="_blank" >10.1016/j.laa.2021.05.010</a>

Result language
angličtina
Original language name
On generalized self-similarities of cut-and-project sets
Original language description
Cut-and-project sets $SigmasubsetR^n$ represent one of the types of uniformly discrete relatively dense sets. They arise by projection of a section of a higherdimensional lattice to a suitably oriented subspace. Cut-and-project sets find application in solid state physics as mathematical models of atomic positions in quasicrystals, the description of their symmetries is therefore of high importance. We focus on the question when a linear map $A$ on $R^n$ is a self-similarity of a cutand- project set $Sigma$, i.e. satisfies $ASigmasubsetSigma$. We characterize such mappings $A$ and provide a construction of a suitable cut-and-project set $Sigma$. We determine minimal dimension of a lattice which permits construction of such a set $Sigma$.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/EF16_019%2F0000778" target="_blank" >EF16_019/0000778: Center for advanced applied science</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach

Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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