We show that the number of geometric permutations of an arbitrary collection of $n$ pair wise disjoint convex sets in $mathbb{R}^d$, for $dgeq 3$, is $O(n^{2d-3}log n)$, improving Wenger's 20 years old bound of $O(n^{2d-2})$.
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机译：我们展示了$ n $配对的任意收集的几何排列数量在$ mathbb {r} ^ d $，$ dgeq 3 $中，$ o（n ^ {2d-3} log n ）$，改善温格的20岁$ o（n ^ {2d-2}）$。
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