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On the Maximum Number of Touching Pairs in a Finite Packing of Translates of a Convex Body

✍ Scribed by Károly Bezdek

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
102 KB
Volume
98
Category
Article
ISSN
0097-3165

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✦ Synopsis

Minkowski space M d =(R d , || ||) is just R d with distances measured using a norm || ||. A norm || || is completely determined by its unit ball {x ¥ R d | ||x|| [ 1} which is a centrally symmetric convex body of the d-dimensional Euclidean space E d . In this note we give upper bounds for the maximum number of times the minimum distance can occur among n points in M d , d \ 3. In fact, we deal with a somewhat more general problem namely, we give upper bounds for the maximum number of touching pairs in a packing of n translates of a given convex body in E d , d \ 3.

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