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Local Packing Phenomena

  • Chuanming Zong
  • James J. Dudziak
Chapter
Part of the Universitext book series (UTX)

Abstract

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)?

Keywords

Packing Density Convex Body Lattice Packing Supporting Hyperplane Independent Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York, Inc. 1996

Authors and Affiliations

  • Chuanming Zong
    • 1
  • James J. Dudziak
    • 2
  1. 1.Institute of MathematicsThe Chinese Academy of SciencesBeijingPR China
  2. 2.Department of MathematicsBucknell UniversityLewisburgUSA

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