不对称但平衡的点配置
Point configurations that are asymmetric yet balanced
摘要：
一个被限制在球体中的粒子的构形是平衡的，如果它在所有的力定律下都处于平衡状态（这些力定律作用在两个点之间，强度由距离的固定函数给出）。很容易证明每一个充分对称的构型都是平衡的，但反过来却很不明显。1957年，利奇对R^3中的平衡构型进行了完全分类，他的分类与R^3中的相反分类是等价的。在本文中，我们反证在高维的逆。我们构造了几个反例，包括一个具有平凡对称群的反例。
英文摘要：
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.
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