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Blichfeldt-type inequalities and central symmetry
-
Martin Henk
,
Matthias Henze
Published/Copyright:
August 22, 2011
Abstract
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.
Received: 2011-06-01
Published Online: 2011-08-22
Published in Print: 2011-November
© de Gruyter 2011
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Keywords for this article
Central symmetry;
zonotope;
crosspolytope;
Ehrhart polynomial;
lattice polytopes
Articles in the same Issue
- Quasigeodesics and farthest points on convex surfaces
- The geometry of canal surfaces and the length of curves in de Sitter space
- On the mutual position of two irreducible conics in PG(2, q), q odd
- On the symmetric average of a convex body
- Ample vector bundles and polarized manifolds of sectional genus three
- Flat Laguerre planes of Kleinewillinghöfer type III.B
- Quotients of hypersurfaces in weighted projective space
- Characterizing the mixed volume
- Uniqueness of lattice packings and coverings of extreme density
- On the classification of convex lattice polytopes
- Blichfeldt-type inequalities and central symmetry
- Valuations on function spaces
