Point configurations that are asymmetric yet balanced
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, bu...
| প্রধান লেখক: | , , , |
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| অন্যান্য লেখক: | |
| বিন্যাস: | প্রবন্ধ |
| ভাষা: | en_US |
| প্রকাশিত: |
American Mathematical Society
2011
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| অনলাইন ব্যবহার করুন: | http://hdl.handle.net/1721.1/60891 https://orcid.org/0000-0001-9261-4656 |
| সংক্ষিপ্ত: | 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. |
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