Duke Mathematical Journal

Mutually contiguous translates of a plane disk

A. Bezdek, K. Kuperberg, and W. Kuperberg

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Article information

Duke Math. J., Volume 78, Number 1 (1995), 19-31.

First available in Project Euclid: 20 February 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 52C15: Packing and covering in $2$ dimensions [See also 05B40, 11H31]
Secondary: 52A30: Variants of convex sets (star-shaped, (m, n)-convex, etc.)


Bezdek, A.; Kuperberg, K.; Kuperberg, W. Mutually contiguous translates of a plane disk. Duke Math. J. 78 (1995), no. 1, 19--31. doi:10.1215/S0012-7094-95-07802-8. https://projecteuclid.org/euclid.dmj/1077285547

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  • [CS] J. H. Conway and N. J. A. Sloane, Sphere packings, lattices and groups, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 290, Springer-Verlag, New York, 1988.
  • [FT] G. Fejes Tóth, New results in the theory of packing and covering, Convexity and its applications eds. P. M. Gruber and J. M. Wills, Birkhäuser, Basel, 1983, pp. 318–359.
  • [Gm] H. Groemer, Abschätzungen für die Anzahl der konvexen Körper, die einen konvexen Körper berühren, Monatsh. Math. 65 (1961), 74–81.
  • [Gb] B. Grünbaum, On a conjecture of H. Hadwiger, Pacific J. Math. 11 (1961), 215–219.
  • [GS] B. Grünbaum and G. C. Shephard, Tilings and patterns, W. H. Freeman and Company, New York, 1987.
  • [H] H. Hadwiger, Über Treffanzahlen bei translationsgleichen Eikörpern, Arch. Math. 8 (1957), 212–213.
  • [HLS] C. Halberg, E. Levin, and E. Straus, On contiguous congruent sets in Euclidean space, Proc. Amer. Math. Soc. 10 (1959), 335–344.
  • [KK] K. Kuperberg and W. Kuperberg, Translates of a starlike plane region with a common point, Intuitive geometry (Szeged, 1991) eds. K. Böröczky and G. Fejes, Colloq. Math. Soc. János Bolyai, vol. 63, North-Holland, Amsterdam, 1994, pp. 205–216.
  • [Mi] H. Minkowski, Dichteste gitterförmige Lagerung kongruenter Körper, Nachr. Ges. Wiss. Göttingen (1904), 311–355.
  • [Mu] J. R. Munkres, Elements of algebraic topology, Addison-Wesley Publishing Company, Menlo Park, CA, 1984.
  • [R] C. A. Rogers, Packing and covering, Cambridge Tracts in Mathematics and Mathematical Physics, No. 54, Cambridge University Press, New York, 1964.
  • [V] H. Voderberg, Zur Zerlegung der Umgebung eines ebenen Bereiches in kongruente, Jahresber. Deutsch. Math.-Verein 46 (1936), 229–231.