几何置换的改进界
Improved Bounds for Geometric Permutations
摘要：
我们证明了$n$中任意一个$n$两两不相交凸集集合的几何置换数为$O(n^{2d-3}\log n)$，改进了Wenger的$O(n^{2d-2})$的20岁界.
英文摘要：
We show that the number of geometric permutations of an arbitrary collection of $n$ pairwise disjoint convex sets in $\mathbb{R}^d$, for $d\geq 3$, is $O(n^{2d-3}\log n)$, improving Wenger's 20 years old bound of $O(n^{2d-2})$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
