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Segments in ball packings

  • M. Henk (a1) and C. Zong (a2)


Denote by Bn the n-dimensional unit ball centred at o. It is known that in every lattice packing of Bn there is a cylindrical hole of infinite length whenever n≥3. As a counterpart, this note mainly proves the following result: for any fixed ε with ε>0, there exist a periodic point set P(n, ε) and a constant c(n, ε) such that Bn + P(n, ε) is a packing in Rn, and the length of the longest segment contained in Rn\{int(εBn) + P(n, ε)} is bounded by c(n, ε) from above. Generalizations and applications are presented.



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Segments in ball packings

  • M. Henk (a1) and C. Zong (a2)


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