Unit Distances and Diameters in Euclidean Spaces
نویسنده
چکیده
We show that the maximum number of unit distances or of diameters in a set of n points in d-dimensional Euclidean space is attained only by specific types of Lenz constructions, for all d ≥ 4 and n sufficiently large, depending on d. As a corollary we determine the exact maximum number of unit distances for all even d ≥ 6, and the exact maximum number of diameters for all d ≥ 4, for all n sufficiently large, depending on d.
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عنوان ژورنال:
- Discrete & Computational Geometry
دوره 41 شماره
صفحات -
تاریخ انتشار 2009