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Multiplicities of interpoint distances in finite planar sets

✍ Scribed by Paul Erdős; Peter C. Fishburn

Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
373 KB
Volume
60
Category
Article
ISSN
0166-218X

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We determine all homogenous linear inequalities satisfied by the numbers of occurrences of the two largest distances among n points in the plane.

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✍ Katalin Vesztergombi 📂 Article 📅 1987 🏛 Elsevier Science 🌐 English ⚖ 383 KB

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