Local Packing Phenomena
Let K be a fixed convex body in R n . 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 R n . Does h(K1 < h(K2) always imply that z(K1) ≤ z(K2)?
KeywordsPacking Density Convex Body Lattice Packing Supporting Hyperplane Independent Point
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