Flexing infinite frameworks with applications to braced Penrose tilings
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F23%3A00360640" target="_blank" >RIV/68407700:21240/23:00360640 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.dam.2022.09.002" target="_blank" >https://doi.org/10.1016/j.dam.2022.09.002</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.dam.2022.09.002" target="_blank" >10.1016/j.dam.2022.09.002</a>
Alternative languages
Result language
angličtina
Original language name
Flexing infinite frameworks with applications to braced Penrose tilings
Original language description
A planar framework – a graph together with a map of its vertices to the plane – is flexible if it allows a continuous deformation preserving the distances between adjacent vertices. Extending a recent previous result, we prove that a connected graph with a countable vertex set can be realized as a flexible framework if and only if it has a so-called NAC-coloring. The tools developed to prove this result are then applied to frameworks where every 4-cycle is a parallelogram, and countably infinite graphs with n-fold rotational symmetry. With this, we determine a simple combinatorial characterization that determines whether the 1-skeleton of a Penrose rhombus tiling with a given set of braced rhombi will have a flexible motion, and also whether the motion will preserve 5-fold rotational symmetry.
Czech name
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Czech description
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Classification
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
Result continuities
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)
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Discrete Applied Mathematics
ISSN
0166-218X
e-ISSN
1872-6771
Volume of the periodical
324
Issue of the periodical within the volume
January
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
17
Pages from-to
1-17
UT code for WoS article
000870462900001
EID of the result in the Scopus database
2-s2.0-85139225953