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A Blichfeldt-Type inequality for the surface area

by Henk, M., Wills, J. M..

Series: 2007-24, Preprints

52C07 Lattices and convex bodies in $n$ dimensions
11H06 Lattices and convex bodies

In 1921 Blichfeldt gave an upper bound on the number of integral points contained in a convex body in terms of the volume of the body. More precisely, he showed that #$(K\cap\Z^n)\leqn! vol(K)+n,$ whenever $K\subset \R^n$ is a convex body containing $n+1$ affinely independent integral points. Here we prove an analogous inequality with respect to the surface area $F(K)$, namely #$(K\cap\Z^n)

Lattice polytopes, volume, surface area