Abstract
Let K be a fixed convex body in Rn. We call the largest number of nonoverlapping translates of K which can be brought into contact with K the kissing number of K and denote it by h(K). A closely related but contrasting concept is the blocking number of K, denoted z(K), which is the smallest number of nonoverlapping translates of K which are in contact with K and prevent any other translate of K from touching K. Concerning kissing numbers and blocking numbers, one can raise the following intuitive problem:
Problem 4.1. Let K1 and K2 be two distinct convex bodies in Rn. Does h(K1 < h(K2) always imply that z(K1) ≤ z(K2)?
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© 1996 Springer-Verlag New York, Inc.
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Zong, C., Dudziak, J.J. (1996). Local Packing Phenomena. In: Dudziak, J.J. (eds) Strange Phenomena in Convex and Discrete Geometry. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8481-6_4
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DOI: https://doi.org/10.1007/978-1-4613-8481-6_4
Publisher Name: Springer, New York, NY
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