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Exploring the rigidity of planar configurations of points and rods
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.ORCID iD: 0000-0002-5040-2089
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.ORCID iD: 0000-0002-7040-4006
2023 (English)In: Discrete Applied Mathematics, ISSN 0166-218X, E-ISSN 1872-6771, Vol. 336, p. 68-82Article in journal (Refereed) Published
Abstract [en]

In this article we explore the rigidity of realizations of incidence geometries consisting of points and rigid rods: rod configurations. We survey previous results on the rigidity of structures that are related to rod configurations, discuss how to find realizations of incidence geometries as rod configurations, and how this relates to the 2-plane matroid. We also derive further sufficient conditions for the minimal rigidity of k-uniform rod configurations and give an example of an infinite family of minimally rigid 3-uniform rod configurations failing the same conditions. Finally, we construct v3-configurations that are flexible in the plane, and show that there are flexible v3-configurations for all sufficiently large values of v.

Place, publisher, year, edition, pages
Elsevier, 2023. Vol. 336, p. 68-82
Keywords [en]
Combinatorial rigidity, Incidence geometry, Rod configuration
National Category
Computer Sciences
Identifiers
URN: urn:nbn:se:umu:diva-208092DOI: 10.1016/j.dam.2023.03.030ISI: 000983170400001Scopus ID: 2-s2.0-85153509834OAI: oai:DiVA.org:umu-208092DiVA, id: diva2:1755672
Funder
Knut and Alice Wallenberg Foundation, 2020.0001Knut and Alice Wallenberg Foundation, 2020.0007Available from: 2023-05-09 Created: 2023-05-09 Last updated: 2024-07-02Bibliographically approved

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Stokes, KlaraÖhman, Lars-Daniel

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