论文标题
五颜六色的特维尔伯格分区的耐受性
Tolerance for colorful Tverberg partitions
论文作者
论文摘要
Tverberg的定理将分区存在的点$ \ mathbb {r}^d $限制为凸起船体相交的$ r $零件所需的点。如果点上有$ n $颜色的颜色，我们寻求分区，每个部分最多都有每种颜色的一个点。在此手稿中，我们绑定了存在分区所需的颜色类数量，即使删除了任何一组$ t $颜色，零件的凸面相交也相交。当$ r \ le d+1 $时，我们证明了$ t $的最佳最佳界限，在$ r> d+1 $时提高已知界限，并为$ t = n-o（n）$的点配置给出几何表征。
Tverberg's theorem bounds the number of points $\mathbb{R}^d$ needed for the existence of a partition into $r$ parts whose convex hulls intersect. If the points are colored with $N$ colors, we seek partitions where each part has at most one point of each color. In this manuscript, we bound the number of color classes needed for the existence of partitions where the convex hulls of the parts intersect even after any set of $t$ colors is removed. We prove asymptotically optimal bounds for $t$ when $r \le d+1$, improve known bounds when $r>d+1$, and give a geometric characterization for the configurations of points for which $t=N-o(N)$.
