Packing Lines, Planes, etc.: Packings in Grassmannian Space
Combinatorics
2007-05-23 v1
Abstract
This paper addresses the question: how should N n-dimensional subspaces of m-dimensional Euclidean space be arranged so that they are as far apart as possible? The results of extensive computations for modest values of N, n, m are described, as well as a reformulation of the problem that was suggested by these computations. The reformulation gives a way to describe n-dimensional subspaces of m-space as points on a sphere in dimension (m-1)(m+2)/2, which provides a (usually) lower-dimensional representation than the Pluecker embedding, and leads to a proof that many of the new packings are optimal. The results have applications to the graphical display of multi-dimensional data via Asimov's "Grand Tour" method.
Cite
@article{arxiv.math/0208004,
title = {Packing Lines, Planes, etc.: Packings in Grassmannian Space},
author = {J. H. Conway and R. H. Hardin and N. J. A. Sloane},
journal= {arXiv preprint arXiv:math/0208004},
year = {2007}
}
Comments
36 pages, 15 figures