Swanepoel, Konrad (2009) Unit distances and diameters in Euclidean spaces. Discrete and computational geometry, 41 (1). pp. 1-27. ISSN 0179-5376
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.
|Additional Information:||© 2009 Springer|
|Library of Congress subject classification:||Q Science > QA Mathematics|
|Sets:||Departments > Mathematics|
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