Simultaneous packing and covering in the euclidean plane

Monatshefte fur Mathematik

Volumn 134, Issue 3, 2002, Pages 247-255

  Zong, Chuanming ^a  

^a PEKING UNIVERSITY   (China)

Author keywords

Convex body; Covering; Minkowski distance; Packing

Indexed keywords

EID: 0010745411     PISSN: 00269255     EISSN: None     Source Type: Journal    
DOI: 10.1007/s605-002-8260-3     Document Type: Article

References (14)

1. Böröczky K (1986) Closest packing and loosest covering of the space with balls. Studia Sci Math Hungar 21: 79-89
2. Butler GJ (1972) Simultaneous packing and covering in Euclidean space. Proc London Math Soc (3) 25: 721-735
3. Fejes Tóth G, Kuperberg W (1993) Packing and covering with convex sets. In: Gruber PM, Wills JM (eds) Handbook of Convex Geometry. Amsterdam: North-Holland, pp 799-860
4. Gruber PM, Lekkerkerker CG (1987) Geometry of Numbers, 2nd ed. Amsterdam: North-Holland
5. Grünbaum B (1961) On a conjecture of H. Hadwiger. Pacific J Math 11: 215-219
6. Henk M (1995) Finite and Infinite Packings. Habilitationsschrift, Universität Siegen
7. n. Proc Steklov Math Inst 152: 237-254
8. Horváth J (1986) Several Problems of n-dimensional Discrete Geometry. PhD Thesis, Steklov Math Inst, Moscow
9. Mahler K (1947) On the minimum determinant and the circumscribed hexagons of a convex domain. Proc Kon Ned Akad Wet 50: 692-703
10. Reinhardt K (1934) Über die dichteste gitterförmige Lagerung kongruenter Bereiche in der Ebene und eine besondere Art konvexer Kurven. Abh Math Sem Hamburg 10: 216-230
11. Rogers CA (1950) A note on coverings and packings. J London Math Soc 25: 327-331
12. Schmidt WM (1961) Zur Lagerung kongruenter Körper in Raum. Monatsh Math 65: 154-158
13. Thompson AC (1996) Minkowski Geometry. Cambridge: Univ Press
14. Zong C (1999) Sphere Packings. New York Berlin Heidelberg: Springer