A SUFFICIENT CONDITION FOR AN EXTREME COVERING OF n-SPACE BY SPHERES
نویسنده
چکیده
The problem of finding the most economical coverings of M-dimensional Euclidean space by equal spheres whose centres form a lattice, which is equivalent to a problem concerning the inhomogeneous minima of positive definite quadratic forms, has been discussed recently by Barnes and Dickson [1]. The reader is referred to [1] for a complete background on the problem. Terms and notations used will be as in that paper. Among other results, Barnes and Dickson proved that if / is an extreme form in the interior of a Voronoi cone A then (i) every extreme form in A is a multiple of / and (ii) / and A have the same group of automorphisms. It is the main object of this paper to extend these results to the following necessary and sufficient condition for extremeness.
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تاریخ انتشار 2008