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...

Full description

Bibliographic Details
Main Authors: Cohn, Henry (Contributor), Elkies, Noam D. (Author), Kumar, Abhinav (Contributor), Shurmann, Achill (Author)
Other Authors: Massachusetts Institute of Technology. Department of Mathematics (Contributor)
Format: Article
Language:English
Published: American Mathematical Society, 2011-02-04T13:12:56Z.
Subjects:
Online Access:Get fulltext
LEADER 01636 am a22002653u 4500
001 60891
042 |a dc 
100 1 0 |a Cohn, Henry  |e author 
100 1 0 |a Massachusetts Institute of Technology. Department of Mathematics  |e contributor 
100 1 0 |a Cohn, Henry  |e contributor 
100 1 0 |a Cohn, Henry  |e contributor 
100 1 0 |a Kumar, Abhinav  |e contributor 
700 1 0 |a Elkies, Noam D.  |e author 
700 1 0 |a Kumar, Abhinav  |e author 
700 1 0 |a Shurmann, Achill  |e author 
245 0 0 |a Point configurations that are asymmetric yet balanced 
260 |b American Mathematical Society,   |c 2011-02-04T13:12:56Z. 
856 |z Get fulltext  |u http://hdl.handle.net/1721.1/60891 
520 |a 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. 
520 |a National Science Foundation (U.S.) (Grant No. DMS-0757765) 
520 |a National Science Foundation (U.S.) (Grant No. DMS-0501029) 
520 |a Deutsche Forschungsgemeinschaft (DFG) (Grant No. SCHU 1503/4-2) 
546 |a en_US 
655 7 |a Article 
773 |t Proceedings of the American Mathematical Society