Unit distances and diameters in Euclidean spaces

Swanepoel, Konrad ORCID: 0000-0002-1668-887X (2009) Unit distances and diameters in Euclidean spaces. Discrete and Computational Geometry, 41 (1). pp. 1-27. ISSN 0179-5376

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Identification Number: 10.1007/s00454-008-9082-x

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
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	09 Oct 2009 09:51
Last Modified:	04 Oct 2025 03:03
URI:	http://eprints.lse.ac.uk/id/eprint/25405

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