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Finite Sphere Packings and the Methods of Blichfeldt and Rankin

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References

  1. U. Betke, M. Henk and J. M. Wills, Finite and infinite packings, J. reine angew. Math., 453 (1994), 165–191.

    Google Scholar 

  2. U. Betke, M. Henk and J. M. Wills, Sausages are good packings, Discrete Comput. Geometry, 13 (1995), 297–311.

    Google Scholar 

  3. H. F. Blichfeldt, The minimum value of quadratic forms, and the closest packing of spheres, Math. Ann., 101 (1929), 605–608.

    Google Scholar 

  4. G. Fejes Tóth, P. Gritzmann and J. M. Wills, Finite sphere packing and sphere covering, Discrete Comput. Geometry, 4 (1989), 19–40.

    Google Scholar 

  5. G. Fejes Tóth, P. Gritzmann and J. M. Wills, On finite multiple packings, Arch. Math., 55 (1990), 407–411.

    Google Scholar 

  6. G. Fejes Tóth and W. Kuperberg, Packing and covering with convex sets, Handbook of Convex Geometry, P. M. Gruber and J. M. Wills eds., North Holland (Amsterdam, 1993).

    Google Scholar 

  7. G. Fejes Tóth and W. Kuperberg, Blichfeldt's density bound revisited, Math. Ann., 295 (1993), 721–727.

    Google Scholar 

  8. P. Gritzmann, Finite Packungon und Überdeckungen, Habilitationsschrift (Siegen, 1984).

    Google Scholar 

  9. P. Gritzmann, Finite packing of equal balls, J. London Math. Soc., 33 (1986), 543–553.

    Google Scholar 

  10. P. M. Gruber and C. G. Lekkerkerker, Geometry of Numbers, North Holland (Amsterdam, 1993).

    Google Scholar 

  11. G. A. Kabatjanski and V. I. Levenstein, Bounds for packings on a sphere and in space, Problems Inform. Transmission, 14 (1978). 1–17.

    Google Scholar 

  12. V. I. Levenstein, On bounds for packings in n-dimensional euclidean space, Dokl. Akad. Nauk SSSR, 245 (1979), 1299–1303; English transl. in Soviet Math. Dokl., 20 (1979), 417—421.

    Google Scholar 

  13. R. A. Rankin, The closest packing of spherical caps in n dimensions, Proc. Glasgow Assoc., 2 (1955) 139–144.

    Google Scholar 

  14. V. M. Sidelnikov, New bounds for densest packings of spheres in n-dimensional euclidean space, Math. USSR Sbornik, 24 (1974) 147–157.

    Google Scholar 

  15. J. M. Wills, Finite sphere packings and sphere coverings; III. Ital. Convexity Meeting, March 1992, Rendiconti Sem. Matem., Messina, Serie II. Suppl., 2 (1993), 91–97.

    Google Scholar 

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Wills, J.M. Finite Sphere Packings and the Methods of Blichfeldt and Rankin. Acta Mathematica Hungarica 75, 337–342 (1997). https://doi.org/10.1023/A:1006501806853

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