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The Isostatic Conjecture

  • Ricky Pollack Memorial Issue
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Abstract

We show that a jammed packing of disks with generic radii, in a generic container, is such that the minimal number of contacts occurs and there is only one dimension of equilibrium stresses, which have been observed with numerical Monte Carlo simulations. We also point out some connections to packings with different radii and results in the theory of circle packings whose graph forms a triangulation of a given topological surface.

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Acknowledgements

This work was partially supported by the National Science Foundation Grant DMS-1564493 for Connelly, Solomonides and Yampolskaya, and National Science Foundation Grant DMS-1564473 for Gortler.

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Authors and Affiliations

  1. Department of Mathematics, Cornell University, Ithaca, NY, 14853, USA

    Robert Connelly, Evan Solomonides & Maria Yampolskaya

  2. School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, 02138, USA

    Steven J. Gortler

Authors
  1. Robert Connelly
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  2. Steven J. Gortler
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  3. Evan Solomonides
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  4. Maria Yampolskaya
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Correspondence to Robert Connelly.

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Dedicated to the memory of Ricky Pollack.

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Connelly, R., Gortler, S.J., Solomonides, E. et al. The Isostatic Conjecture. Discrete Comput Geom 64, 734–758 (2020). https://doi.org/10.1007/s00454-018-00051-0

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  • DOI: https://doi.org/10.1007/s00454-018-00051-0

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