Duke Mathematical Journal

Mutually contiguous translates of a plane disk

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

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Article information

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

Dates
First available in Project Euclid: 20 February 2004

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1077285547

Digital Object Identifier
doi:10.1215/S0012-7094-95-07802-8

Mathematical Reviews number (MathSciNet)
MR1328750

Zentralblatt MATH identifier
0829.52008

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

Citation

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


Export citation

References

  • [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.