The number of unit distances is almost linear for most norms
نویسنده
چکیده
We prove that there exists a norm in the plane under which no n-point set determines more than O(n log n log logn) unit distances. Actually, most norms have this property, in the sense that their complement is a meager set in the metric space of all norms (with the metric given by the Hausdorff distance of the unit balls).
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تاریخ انتشار 2010