Lattice width directions and Minkowski's 3^d-theorem
Combinatorics
2017-10-10 v1
Abstract
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.
Keywords
Cite
@article{arxiv.0901.1375,
title = {Lattice width directions and Minkowski's 3^d-theorem},
author = {Jan Draisma and Tyrrell B. McAllister and Benjamin Nill},
journal= {arXiv preprint arXiv:0901.1375},
year = {2017}
}
Comments
1 figure, 10 pages