A Minkowski space M-d = (R-d, parallel to parallel to) is just R-d with distances measured using a norm parallel to parallel to. A norm parallel to parallel to is completely determined by its unit ball {x is an element of R-d parallel toxparallel to less than or equal to 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 greater than or equal to 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 greater than or equal to 3. (C) 2002 Elsevier Science (USA). [References: 13]
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