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Covering convex bodies by translates of convex bodies

Part of: General convexity

Published online by Cambridge University Press:  26 February 2010

C. A. Rogers  and
C. Zong
C. A. Rogers
Affiliation:
Department of Mathematics, University College London, Gower Street, London, WC1E 6BT.
C. Zong
Affiliation:
Institute of Mathematics, The Chinese Academy of Sciences, Beijing 100080, China.
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Abstract

A number of known estimates of the number of translates, or lattice translates, of a convex body H required to cover a convex body K are obtained as consequences of two simple results.

MSC classification

Secondary: 52A40: Inequalities and extremum problems
Type
Research Article
Information
Mathematika , Volume 44 , Issue 1 , June 1997 , pp. 215 - 218
Copyright
Copyright © University College London 1997

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References

1.Bezdek, K.. Hadwiger Levi's covering problem revisited. New Trends in Discrete and Computational Geometry (Pach, J., ed.) (Springer-Verlag, Berlin, 1994), pp. 199–233.Google Scholar
2.Bezdek, K.. On affine subspaces that illuminate a convex set. Beitrdge Algebra Geom., 35 (1994), 131–139.Google Scholar
3.Boltjanski, V. G. and Gohberg, I.. Results and Problems in Combinatorial Geometry (Cambridge University Press, 1985).CrossRefGoogle Scholar
4.Chakerian, G. D. and Stein, S. K.. On the measures of symmetry of convex bodies. Canad. J. Math., 17 (1965), 497–504.CrossRefGoogle Scholar
5.Grünbaum, B.. Measures of symmetry for convex sets. Proc. Svmpos. Pure Math., 1 (1963), 233–270.CrossRefGoogle Scholar
6.Hadwiger, H.. Ungeloste Problems no. 20. Elem. Math., 12 (1957), 121.Google Scholar
7.Rogers, C. A.. A note on coverings. Mathematika, 4 (1957), 1–6.CrossRefGoogle Scholar
8.Rogers, C. A.. Lattice coverings of space. Mathematika, 6 (1959), 33–39.CrossRefGoogle Scholar
9.Rogers, C. A.. Packing and Covering (Cambridge University Press, 1964).Google Scholar
10.Rogers, C. A. and Shephard, G. C.. The difference body of a convex body. Arch. Math., 8 (1958), 220–233.CrossRefGoogle Scholar
11.Zong, C.. Some remarks concerning kissing numbers, blocking numbers and covering numbers. Period. Math. Hungar., 30 (1995), 233–23CrossRefGoogle Scholar