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Thinnest Packing of Cubes with a Given Number of Neighbours

Published online by Cambridge University Press:  20 November 2018

L. Fejes Tóth  and
N. Sauer
L. Fejes Tóth
Affiliation:
Mathematical Institute of the Hungarian Academy of Sciences Budapest V., Reáltanova U. 13-15
N. Sauer
Affiliation:
Dept. of Mathematics University of Calgary, Calgary, Alberta Canada T2N 1N4
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As a contribution to various investigations [1-11] about packing of convex bodies with certain conditions imposed on the number of neighbours of each body, V. Chvátal [12] recently proved the following theorem: If in a packing of translates of a square each square has at least six neighbours then the density of the packing is at least 11/15.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 20 , Issue 4 , 01 December 1977 , pp. 501 - 507
Copyright
Copyright © Canadian Mathematical Society 1977

References

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