05-22
Ehrhart polynomial and Successive Minima
by Henk, M; Sch\xfcrmann, A.; Wills, J.M.
Preprint series: 05-22, 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: We investigate the Ehrhart polynomial for the class of 0-symmetric convex lattice polytopes in Euclidean n-space \R^n. It turns out that the roots of the Ehrhart polynomial and Minkowski\'s successive minima are closely related by their geometric and arithmetic mean. We also show that the roots of lattice $n$-polytopes with or without interior lattice points differ essentially. Furthermore, we study the structure of the roots in the planar case. Here it turns out that their distribution reflects basic properties of lattice polygons.
Keywords: Lattice polytopes, successive minima, Ehrhart polynomial
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