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Unit distances and diameters in Euclidean spaces

Swanepoel, Konrad (2009) Unit distances and diameters in Euclidean spaces. Discrete and Computational Geometry, 41 (1). pp. 1-27. ISSN 0179-5376

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Abstract

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 and all n sufficiently large depending on d.

Item Type: Article
Official URL: http://www.springer.com/math/numbers/journal/454
Additional Information: © 2009 Springer
Library of Congress subject classification: Q Science > QA Mathematics
Sets: Departments > Mathematics
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 09 Oct 2009 09:51
URL: http://eprints.lse.ac.uk/25405/

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