2 O ct 2 00 0 Lattice Points in Lattice Polytopes

@inproceedings{Pikhurko20082OC,
  title={2 O ct 2 00 0 Lattice Points in Lattice Polytopes},
  author={Oleg Pikhurko},
  year={2008}
}
We show that, for any lattice polytope P ⊂ R, the set int(P ) ∩ lZ (provided it is non-empty) contains a point whose coefficient of asymmetry with respect to P is at most 8d · (8l+7) 2d+1 . If, moreover, P is a simplex, then this bound can be improved to 8 · (8l + 7) d+1 . As an application, we deduce new upper bounds on the volume of a lattice polytope, given its dimension and the number of sublattice points in its interior. 

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