Blichfeldt-type inequalities and central symmetry

A classical result of Blichfeldt, from 1921, gives a sharp lower bound on the volume of a convex body K, whose lattice points span the whole space, in terms of the lattice point enumerator . We are interested in a version of this inequality on the set of 0-symmetric convex bodies. Our motivation to...

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Bibliographic Details
Published in:Advances in geometry 2011-11, Vol.11 (4), p.731-744
Main Authors: Henk, Martin, Henze, Matthias, Wills, Jörg M.
Format: Article
Language:English
Subjects:
Central symmetry
crosspolytope
Ehrhart polynomial
lattice polytopes
zonotope
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Summary:A classical result of Blichfeldt, from 1921, gives a sharp lower bound on the volume of a convex body K, whose lattice points span the whole space, in terms of the lattice point enumerator . We are interested in a version of this inequality on the set of 0-symmetric convex bodies. Our motivation to study this problem comes from a lack of methods that exploit the symmetry assumption in problems of a similar kind and where 0-symmetry is a natural condition. We report upon sharp Blichfeldt-type inequalities for 0-symmetric lattice polygons, lattice crosspolytopes and lattice zonotopes.
ISSN:1615-715X
1615-7168
DOI:10.1515/advgeom.2011.032