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1996 Packing lines, planes, etc.: packings in Grassmannian spaces
John H. Conway, Ronald H. Hardin, Neil J. A. Sloane
Experiment. Math. 5(2): 139-159 (1996).

Abstract

We address 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 $\half(m-1) (m+2)$, which provides a (usually) lower-dimensional 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 multi-dimensional data via Asimov's grand tour method.

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John H. Conway. Ronald H. Hardin. Neil J. A. Sloane. "Packing lines, planes, etc.: packings in Grassmannian spaces." Experiment. Math. 5 (2) 139 - 159, 1996.

Information

Published: 1996
First available in Project Euclid: 13 March 2003

zbMATH: 0864.51012
MathSciNet: MR1418961

Subjects:
Primary: 52C17
Secondary: 65Y25

Rights: Copyright © 1996 A K Peters, Ltd.

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Vol.5 • No. 2 • 1996
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