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Applying the pebble game algorithm to rod configurations
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.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.ORCID iD: 0000-0002-7040-4006
2023 (English)In: EuroCG 2023: Book of abstracts, 2023, article id 41Conference paper, Published paper (Refereed)
Abstract [en]

We present results on rigidity of structures of rigid rods connected in joints: rod configurations. The underlying combinatorial structure of a rod configuration is an incidence structure. Our aim is to find simple ways of determining which rod configurations admit non-trivial motions, using the underlying incidence structure.

Rigidity of graphs in the plane is well understood. Indeed, there is a polynomial time algorithm for deciding whether most realisations of a graph are rigid. One of the results presented here equates rigidity of sufficiently generic rod configurations to rigidity of a related graph. As a consequence, itis possible to determine the rigidity of rod configurations using the previously mentioned polynomial time algorithm. We use this to show that all v3-configurations on up to 15 points and all triangle-free v3-configurations on up to 20 points are rigid in regular position, if such a realisation exists. We also conjecture that the smallest v3-configuration that is flexible in regular position is a previously known 283-configuration. 

Place, publisher, year, edition, pages
2023. article id 41
National Category
Discrete Mathematics Geometry
Identifiers
URN: urn:nbn:se:umu:diva-215548OAI: oai:DiVA.org:umu-215548DiVA, id: diva2:1806504
Conference
The 39th European workshop on computational geometry (EuroCG 2023), Barcelona, Spain, March 29-31, 2023
Available from: 2023-10-22 Created: 2023-10-22 Last updated: 2023-10-23Bibliographically approved

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EuroCG 2023

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Lundqvist, SigneStokes, KlaraÖhman, Lars-Daniel

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