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A Bound on the Ratio between the Packing and Covering Densities of a Convex Body (2000)

Smith, E. H.

Springer

Discrete & computational geometry 23 (2000), S. 325-331

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ISSN: 1432-0444

Source: Springer Online Journal Archives 1860-2000

Topics: Computer Science , Mathematics

Notes: Abstract. It is shown that if K is a compact convex set which is centrally symmetric and has a nonempty interior, then the density of the tightest lattice packing with copies of K in Euclidean 3-space divided by the density of the thinnest lattice covering of Euclidean 3-space with copies of K is greater than or equal to 1/4. It is likely this bound can be improved, though not beyond approximately 1/2.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/PL00009503

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