Finite sphere packing and sphere covering |
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Authors: | G Fejes Tóth P Gritzmann J M Wills |
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Institution: | (1) Mathematical Institute of the Hungarian Academy of Sciences, Reáltanoda u. 13-15, H-1053 Budapest, Hungary;(2) Mathematical Institute of the University of Siegen, Hoelderlinstrasse 3, D-5900 Siegen, Federal Republic of Germany |
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Abstract: | A basic problem of finite packing and covering is to determine, for a given number ofk unit balls in Euclideand-spaceE
d
, (1) the minimal volume of all convex bodies into which thek balls can be packed and (2) the maximal volume of all convex bodies which can be covered by thek balls. In the sausage conjectures by L. Fejes Tóth and J. M. Wills it is conjectured that, for alld 5, linear arrangements of thek balls are best possible. In the paper several partial results are given to support both conjectures. Furthermore, some relations between finite and infinite (space) packing and covering are investigated.This paper was written while the first named author was visiting the Forschungsinstitut für Geistes- und Sozialwissenschaften at the University of Siegen. |
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