Distance Sets of Well-Distributed Planar Point Sets
نویسندگان
چکیده
We prove that a well-distributed subset of R2 can have a distance set ∆ with #(∆ ∩ [0, N ]) ≤ CN3/2− only if the distance is induced by a polygon K. Furthermore, if the above estimate holds with = 1/2, then K can have only finitely many sides.
منابع مشابه
Distance Sets of Well-distributed Planar Sets for Polygonal Norms
Let X be a 2-dimensional normed space, and let BX be the unit ball in X. We discuss the question of how large the set of extremal points of BX may be if X contains a well-distributed set whose distance set ∆ satisfies the estimate |∆ ∩ [0, N ]| ≤ CN3/2− . We also give a necessary and sufficient condition for the existence of a well-distributed set with |∆ ∩ [0, N ]| ≤ CN .
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عنوان ژورنال:
- Discrete & Computational Geometry
دوره 31 شماره
صفحات -
تاریخ انتشار 2004