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Applying the pebble game algorithm to rod configurations
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.ORCID-id: 0000-0002-7040-4006
2023 (engelsk)Inngår i: EuroCG 2023: Book of abstracts, 2023, artikkel-id 41Konferansepaper, Publicerat paper (Fagfellevurdert)
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. 

sted, utgiver, år, opplag, sider
2023. artikkel-id 41
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URN: urn:nbn:se:umu:diva-215548OAI: oai:DiVA.org:umu-215548DiVA, id: diva2:1806504
Konferanse
The 39th European workshop on computational geometry (EuroCG 2023), Barcelona, Spain, March 29-31, 2023
Tilgjengelig fra: 2023-10-22 Laget: 2023-10-22 Sist oppdatert: 2023-10-23bibliografisk kontrollert

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Lundqvist, SigneStokes, KlaraÖhman, Lars-Daniel

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