2002/08/01 by J. H. Conway, R. H. Hardin, N. J. A. Sloane · 3 citations
Mathematics · #math.CO #msc:51E15 #msc:52C17
published as Experimental Mathematics, 5 (1996), 139-159 · 36 pages, 15 figures
arxiv created 2002/08/01 · arxiv updated 2009/11/30
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.