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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

  • Czech description

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