Lattice width directions and Minkowski's 3^d-theorem

Details Lattice width directions and Minkowski's 3^d-theorem Lattice width directions and Minkowski's 3^d-theorem

2009-01-10

arxiv.org/abs/0901.1375v1

Mathematics

Combinatorics

1 figure, 10 pages

Scientific paper

We show that the number of lattice directions in which a d-dimensional convex
body in R^d has minimum width is at most 3^d-1, with equality only for the
regular cross-polytope. This is deduced from a sharpened version of the
3^d-theorem due to Hermann Minkowski (22 June 1864--12 January 1909), for which
we provide two independent proofs.

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