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Covering a Ball by Smaller Balls

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Abstract

We prove that, for any covering of a unit d-dimensional Euclidean ball by smaller balls, the sum of radii of the balls from the covering is greater than d. We also investigate the problem of finding lower and upper bounds for the sum of powers of radii of the balls covering a unit ball.

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Acknowledgements

The author would like to thank Arseniy Akopyan and Alexandr Polyanskii for bringing this problem to his attention and for invaluable discussions. The author was supported in part by NSF Grant DMS-1400876.

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Authors and Affiliations

  1. School of Mathematical & Statistical Sciences, The University of Texas Rio Grande Valley, Brownsville, TX, 78520, USA

    Alexey Glazyrin

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  1. Alexey Glazyrin
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Correspondence to Alexey Glazyrin.

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Editor in Charge: János Pach

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Glazyrin, A. Covering a Ball by Smaller Balls. Discrete Comput Geom 62, 781–787 (2019). https://doi.org/10.1007/s00454-018-0010-4

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  • DOI: https://doi.org/10.1007/s00454-018-0010-4

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