Studia Scientiarum Mathematicarum Hungarica
Volume/Issue:
Volume 61: Issue 4
Universal Rigidity of Ladders on the Line
Authors:
Bryan Gin-ge Chen Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA, USA

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,
Robert Connelly Department of Mathematics, Cornell University, Ithaca, NY, USA

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Steven J. Gortler School of Engineering and Applied Sciences, Harvard University, Cambridge, USA

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Anthony Nixon School of Mathematical Sciences, Lancaster University, Lancaster, UK

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Louis Theran School of Mathematics and Statistics, University of St Andrews, St. Andrews, United Kingdom

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Pages:
377–399
Online Publication Date:
18 Dec 2024
Publication Date:
08 Jan 2025
Article Category:
Research Article
DOI:
https://doi.org/10.1556/012.2024.04322
Keywords:
Universal rigidity; bar-joint framework; ladder framework; super stability
Restricted access

In [3] it is shown, answering a question of Jordán and Nguyen [9], that universal rigidity of a generic bar-joint framework in ℝ1 depends on more than the ordering of the vertices. The graph 𝐺 that was used in that paper is a ladder with three rungs. Here we provide a general answer when that ladder with three rungs in the line is universally rigid and when it is not.

  • [1]

    A. Y. Alfakih. On dimensional rigidity of bar-and-joint frameworks. Discrete Appl. Math., 155(10):1244–1253, 2007.

  • [2]

    A. Y. Alfakih. On bar frameworks, stress matrices and semidefinite programming. Mathematical programming, 129(1):113–128, 2011.

  • [3]

    B. Chen, R. Connelly, A. Nixon, and L. Theran. Universal rigidity on the line, point order. arXiv:2104.01892, 2021.

  • [4]

    R. Connelly. Rigidity and energy. Invent. Math., 66(1):11–33, 1982.

  • [5]

    R. Connelly and S. J. Gortler. Iterative universal rigidity. Discrete Comput. Geom., 53(4):847–877, 2015.

  • [6]

    R. Connelly and S. D. Guest. Frameworks, tensegrities, and symmetry. Cambridge University Press, Cambridge, 2022.

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    H. S. M. Coxeter. Introduction to geometry. Wiley Classics Library. John Wiley & Sons, Inc., New York, 1989. Reprint of the 1969 edition.

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  • [8]

    S. J. Gortler and D. P. Thurston. Characterizing the universal rigidity of generic frameworks. Discrete Comput. Geom., 51(4):1017–1036, 2014.

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    • Export Citation
  • [9]

    T. Jordán and V.-H. Nguyen. On universally rigid frameworks on the line. Contrib. Discrete Math., 10(2):10–21, 2015.

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Cover Studia Scientiarum Mathematicarum Hungarica
Studia Scientiarum Mathematicarum Hungarica
Print ISSN:
0081-6906
Online ISSN:
1588-2896

Editors in Chief

Gábor SIMONYI (Rényi Institute of Mathematics)
András STIPSICZ (Rényi Institute of Mathematics)
Géza TÓTH (Rényi Institute of Mathematics) 

Managing Editor

Gábor SÁGI (Rényi Institute of Mathematics)

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  • Imre BÁRÁNY (Rényi Institute of Mathematics)
  • Károly BÖRÖCZKY (Rényi Institute of Mathematics and Central European University)
  • Péter CSIKVÁRI (ELTE, Budapest) 
  • Joshua GREENE (Boston College)
  • Penny HAXELL (University of Waterloo)
  • Andreas HOLMSEN (Korea Advanced Institute of Science and Technology)
  • Ron HOLZMAN (Technion, Haifa)
  • Satoru IWATA (University of Tokyo)
  • Tibor JORDÁN (ELTE, Budapest)
  • Roy MESHULAM (Technion, Haifa)
  • Frédéric MEUNIER (École des Ponts ParisTech)
  • Márton NASZÓDI (ELTE, Budapest)
  • Eran NEVO (Hebrew University of Jerusalem)
  • János PACH (Rényi Institute of Mathematics)
  • Péter Pál PACH (BME, Budapest)
  • Andrew SUK (University of California, San Diego)
  • Zoltán SZABÓ (Princeton University)
  • Martin TANCER (Charles University, Prague)
  • Gábor TARDOS (Rényi Institute of Mathematics)
  • Paul WOLLAN (University of Rome "La Sapienza")

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Studia Scientiarum Mathematicarum Hungarica
Language English
French
German
Size B5
Year of
Foundation		 1966
Volumes
per Year		 1
Issues
per Year		 4
Founder Magyar Tudományos Akadémia  
Founder's
Address		 H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Publisher's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
Responsible
Publisher		 Chief Executive Officer, Akadémiai Kiadó
ISSN 0081-6906 (Print)
ISSN 1588-2896 (Online)

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