Let S be a set of n red and n blue points in general position in ${\mathbb{R}}^3$. Let τ be a tetrahedron with vertices in S. We say that τ is empty if it does not contain any point of S in its interior. We say that τ is balanced if two of its vertices are blue, and two of its vertices are red. In this paper we show that S spans $\mathrm{\Omega }(n^{5/2})$ empty balanced tetrahedra.

中文翻译：

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关于空平衡四面体中两个彩色点集的注释 ${\mathbb{[R}}^3$

令S为在一般位置的n个红色和n个蓝色点的集合${\mathbb{[R}}^3$。令τ为S中具有顶点的四面体。我们说，如果τ在其内部不包含S的任何点，则为空。我们说，如果τ的两个顶点为蓝色，而两个顶点为红色，则τ是平衡的。在本文中，我们表明S跨度$\mathrm{\Omega }（{ñ}^{5/2}）$ 空的平衡四面体。