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On uniform boundedness of a rational distance set in the plane

โœ Scribed by Mehdi Makhul; Jafar Shaffaf


Book ID
116389966
Publisher
Elsevier Science
Year
2012
Tongue
English
Weight
126 KB
Volume
350
Category
Article
ISSN
1631-073X

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On the distribution of distances in fini
โœ K Vesztergombi ๐Ÿ“‚ Article ๐Ÿ“… 1985 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 894 KB

Let n k denote the number of times the kth largest distance occurs among a set S of n points. We show that if S is the set of vertices of a convex polygone in the euclidean plane, then n1+2n2~3n and n2<~n +n 1. Together with the well-known inequality n~<~n and the trivial inequalities n~>~O and n2>~