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Packings, Coverings, Partitionings, and Certain Other Distributions in Spaces of Constant Curvature

  • E. P. Baranovskii
Part of the Progress in Mathematics book series (PM, volume 9)

Abstract

A set {Ki} of bodies Ki forms a packing in a domain D if \( \mathop \cup \limits_i {K_i} \subset D \) and no two bodies of set {Ki} have common interior points. Sometimes a packing is called a filling and in the Russian translation of Cassels’ book [26] the term “stacking” is used. If no two bodies K i and Kj have common interior points and \( \mathop \cup \limits_i {K_i} = D \), then we speak of the partitioning of domain D into bodies Ki. The set {Ki} forms a covering of domain D, or covers domain D, if \( \mathop \cup \limits_i {K_i} \supset D \). In the definitions listed above it is understood that the domain D can coincide with the whole space in which it is located.

Keywords

Dense Packing Convex Body Lattice Packing Lattice Covering Regular Partitionings 
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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© Plenum Press, New York 1971

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  • E. P. Baranovskii

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