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Bounds on the lattice point enumerator via slices and projections (2004.14097v2)
Published 29 Apr 2020 in math.MG
Abstract: Gardner, Gronchi and Zong posed the problem to find a discrete analogue of M. Meyer's inequality bounding the volume of a convex body from below by the geometric mean of the volumes of its slices with the coordinate hyperplanes. Motivated by this problem, for which we provide a first general bound, we study in a more general context the question to bound the number of lattice points of a convex body in terms of slices as well as projections.
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