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On distance sets of large sets of integer points

✍ Scribed by Ákos Magyar

Book ID: 107529053
Publisher: The Hebrew University Magnes Press
Year: 2008
Tongue: English
Weight: 174 KB
Volume: 164
Category: Article
ISSN: 0021-2172
DOI: 10.1007/s11856-008-0028-z

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Let n k denote the number of times the kth largest distance occurs among a set S of n points in the Euclidean plane. We prove that n2 ~< 2~n for arbitrary set S. This upper bound is sharp. We consider the set S of n arbitrary points in R 2. We denote the largest distance between two points in S by