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We find tight estimates for the minimum number of proper subspaces needed to cover all lattice points in an n-dimensional convex body C, symmetric about the origin 0. This enables us to prove the following statement, which settles a problem of G. Halász. The maximum number of n-wise linearly independent lattice points in the n-dimensional ball rB n of… (More)

Let m(n) denote the smallest integer m with the property that any set of n points in Euclidean 3-space has an element such that at most m other elements are equidistant from it. We have that cn 1=3 log log n6m(n)6n 3=5 ÿ(n); where c¿0 is a constant and ÿ(n) is an extremely slowly growing function, related to the inverse of the Ackermann function.

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