论文标题
$ \ mathbb {r}^3 $中的两个有色点集中的空平衡四面体上的注释
A Note on Empty Balanced Tetrahedra in Two colored Point sets in $\mathbb{R}^3$
论文作者
论文摘要
令$ s $为$ n $ red和$ n $蓝点的一组，在$ \ mathbb {r}^3 $中处于一般位置。令$τ$为$ s $的顶点的四面体。我们说$τ$是\ emph {empty}，如果它不包含其内部$ s $的任何点。我们说$τ$是\ emph {balanced}，如果它包含两个蓝色顶点和两个红色顶点。在本文中，我们表明$ s $跨度$ω（n^{5/2}）$空平衡四面体。
Let $S$ be a set of $n$ red and $n$ blue points in general position in $\mathbb{R}^3$. Let $τ$ be a tetrahedra with vertices on $S$. We say that $τ$ is \emph{empty} if it does not contain any point of $S$ in its interior. We say that $τ$ is \emph{balanced} if it contains two blue vertices and two red vertices. In this paper we show that $S$ spans $Ω(n^{5/2})$ empty balanced tetrahedra.
