Lattice Bounded Distance Equivalence for 1D Delone Sets with Finite Local Complexity

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F21%3A00351619" target="_blank" >RIV/68407700:21340/21:00351619 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.7546/jgsp-59-2021-1-29" target="_blank" >https://doi.org/10.7546/jgsp-59-2021-1-29</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.7546/jgsp-59-2021-1-29" target="_blank" >10.7546/jgsp-59-2021-1-29</a>

Result language
angličtina
Original language name
Lattice Bounded Distance Equivalence for 1D Delone Sets with Finite Local Complexity
Original language description
Spectra of suitably chosen Pisot-Vijayaraghavan numbers represent non-trivial examples of self-similar Delone point sets of finite local complexity, indispensable in quasicrystal modeling. For the case of quadratic Pisot units, we characterize, dependingly on digits in the corresponding numeration systems, the spectra which are bounded distance to an average lattice. Our method stems in the interpretation of the spectra in the frame of the cut-and-project method. Such structures are coded by an infinite word over a finite alphabet which enables us to exploit combinatorial notions such as balancedness, substitutions, and the spectrum of associated incidence matrices.
Czech name
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Czech description
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Type
J<sub>SC</sub> - Article in a specialist periodical, which is included in the SCOPUS 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)

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

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