Swanepoel, Konrad (2009) Unit distances and diameters in Euclidean spaces. Discrete and Computational Geometry, 41 (1). pp. 1-27. ISSN 0179-5376
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 |
| Date Deposited: | 09 Oct 2009 09:51 |
| URL: | http://eprints.lse.ac.uk/25405/ |
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