Packing Lines, Planes, etc.: Packings in Grassmannian Spaces

We addressthe question: How should N n-dimensional subspaces of m-dimensional Euclidean space be arranged so that they are as far apart as possible? The resuIts 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...

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Bibliographic Details
Published in:Experimental mathematics 1996-01, Vol.5 (2), p.139-159
Main Authors: Conway, John H., Hardin, Ronald H., Sloane, Neil J. A.
Format: Article
Language:English
Subjects:
52C17
65Y25
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Summary:We addressthe question: How should N n-dimensional subspaces of m-dimensional Euclidean space be arranged so that they are as far apart as possible? The resuIts 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 ½(m-l)(m+2), which provides a (usually) lowerdimensional representation than the Plücker embedding, and leads to a proof that many of the new packings are optimal. The results have applications to the graphical display of multidimensional data via Asimov's grand tour method.
ISSN:1058-6458
1944-950X
DOI:10.1080/10586458.1996.10504585