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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the best constant for the Besicovitch covering theorem


Authors: Zoltán Füredi and Peter A. Loeb
Journal: Proc. Amer. Math. Soc. 121 (1994), 1063-1073
MSC: Primary 28A75; Secondary 05B40, 52C17
MathSciNet review: 1249875
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Abstract: This note shows that in terms of known proofs of the Besicovitch Covering Theorem, the best constant for that theorem is the maximum number of points that can be packed into a closed ball of radius 2 when the distance between pairs of points is at least 1 and one of the points is at the center of the ball. Exponential upper and lower bounds are also established.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1249875-4
PII: S 0002-9939(1994)1249875-4
Keywords: Besicovitch Covering Theorem, sphere packings, proximity graphs
Article copyright: © Copyright 1994 American Mathematical Society