dc.contributor.author Cohn, Henry dc.contributor.author Kumar, Abhinav dc.contributor.author Elkies, Noam David dc.contributor.author Schürmann, Achill dc.date.accessioned 2011-11-22T17:30:53Z dc.date.issued 2010 dc.identifier.citation Cohn, Henry, Elkies, Noam, Kumar, Abhinav, and Achill Schuermann. 2010. Point configurations that are asymmetric yet balanced. Proceedings of the American Mathematical Society 138 (2010): 2863-2872. en_US dc.identifier.issn 1088-6826 en_US dc.identifier.issn 0002-9939 en_US dc.identifier.uri http://nrs.harvard.edu/urn-3:HUL.InstRepos:5351575 dc.description.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 $R^3$, and his classification is equivalent to the converse for $R^3$. In this paper we disprove the converse in high dimensions. We construct several counterexamples, including one with trivial symmetry group. en_US dc.description.sponsorship Mathematics en_US dc.language.iso en_US en_US dc.publisher American Mathematical Society en_US dc.relation.isversionof doi://10.1090/S0002-9939-10-10284-6 en_US dash.license OAP dc.title Point Configurations That Are Asymmetric Yet Balanced en_US dc.type Journal Article en_US dc.description.version Author's Original en_US dc.relation.journal Proceedings of the American Mathematical Society en_US dash.depositing.author Elkies, Noam David dc.date.available 2011-11-22T17:30:53Z dc.identifier.doi 10.1090/S0002-9939-10-10284-6 * dash.authorsordered false dash.contributor.affiliated Elkies, Noam
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