Lattice Points in Lattice Polytopes
نویسنده
چکیده
We show that, for any lattice polytope P ⊂ R, the set int(P ) ∩lZ (provided it is non-empty) contains a point whose coefficient ofasymmetry 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 ofa lattice polytope, given its dimension and the number of sublatticepoints in its interior.
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