07-24
A Blichfeldt-Type inequality for the surface area
Preprint series: 07-24, Preprints
- MSC:
- 52C07 Lattices and convex bodies in $n$ dimensions, See Also {11H06, 11H31, 11P21}
- 11H06 Lattices and convex bodies, See also {11P21, 52C05, 52C07}
Abstract: 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)
Keywords: Lattice polytopes, volume, surface area
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