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  Covering lattice points by subspaces [1 citations — 0 self]

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by Imre Bárány, Gergely Harcos, János Pach, Gábor Tardos
Period. Math. Hungar
http://www.math.princeton.edu/~gharcos/racs0912.pdf
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Abstract:

Abstract. 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 radius r around 0 is O(r n/(n−1)). This bound cannot be improved. We also show that the order of magnitude of the number of different (n − 1)-dimensional subspaces induced by the lattice points in rB n is r n(n−1).

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