Point configurations that are asymmetric yet balanced
Name
Cohn_Point configurations.pdf
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Author(s)
Cohn, Henry
Elkies, Noam D.
Kumar, Abhinav
Shurmann, Achill
Date Issued
March 2010
Journal
Proceedings of the American Mathematical Society
Publisher
American Mathematical Society
Citation
Cohn, Henry. et al. "Point configurations that are asymmetric yet balanced ." Proc. Amer. Math. Soc. 138 (2010): 2863-2872.
Version
Author's final manuscript
Abstract
Abstract: A configuration of particles confined to a sphere is balanced if it is in equilibrium under all force laws (that act between pairs of points with strength given by a fixed function of distance). It is straightforward to show that every sufficiently symmetrical configuration is balanced, but the converse is far from obvious. In 1957 Leech completely classified the balanced configurations in $ \mathbb{R}^3$, and his classification is equivalent to the converse for $ \mathbb{R}^3$. In this paper we disprove the converse in high dimensions. We construct several counterexamples, including one with trivial symmetry group.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Attribution-Noncommercial-Share Alike 3.0 Unported
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DOI of Published Version
https://doi.org/10.1090/S0002-9939-10-10284-6
