Successive minima, intrinsic volumes, and lattice determinants
نویسندگان
چکیده
منابع مشابه
Intrinsic Volumes and Successive Radii
Motivated by a problem of Teissier to bound the intrinsic volumes of a convex body in terms of the inradius and the circumradius of the body, we give upper and lower bounds for the intrinsic volumes of a convex body in terms of the elementary symmetric functions of the so called successive inner and outer radii. These results improve on former bounds and, in particular, they also provide bounds...
متن کاملLattice Points in Large Borel Sets and Successive Minima
Let B be a Borel set in E with volume V (B) = ∞. It is shown that almost all lattices L in E contain infinitely many pairwise disjoint d-tuples, that is sets of d linearly independent points in B. A consequence of this result is the following: let S be a star body in E with V (S) = ∞. Then for almost all lattices L in E the successive minima λ1(S,L), . . . , λd(S,L) of S with respect to L are 0...
متن کامل2 00 2 Successive Minima and Lattice Points
The main purpose of this note is to prove an upper bound on the number of lattice points of a centrally symmetric convex body in terms of the successive minima of the body. This bound improves on former bounds and narrows the gap towards a lattice point analogue of Minkowski’s second theorem on successive minima. Minkowski’s proof of his second theorem is rather lengthy and it was also criticis...
متن کاملIntrinsic Volumes and Lattice Points of Crosspolytopes
Hadwiger showed by computing the intrinsic volumes of a regular simplex that a rectangular simplex is a counterexample to Wills’s conjecture for the relation between the lattice point enumerator and the intrinsic volumes in dimensions not less than 441. Here we give formulae for the volumes of spherical polytopes related to the intrinsic volumes of the regular crosspolytope and of the rectangul...
متن کاملSuccessive Minima and Radii
In this note we present inequalities relating the successive minima of a o-symmetric convex body and the successive inner and outer radii of the body. These inequalities build a bridge between known inequalities involving only either the successive minima or the successive radii.
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 1995
ISSN: 0179-5376,1432-0444
DOI: 10.1007/bf02574040