Experimental Mathematics

Packing lines, planes, etc.: packings in Grassmannian spaces

John H. Conway, Ronald H. Hardin, and Neil J. A. Sloane

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.

Article information

Source
Experiment. Math., Volume 5, Issue 2 (1996), 139-159.

Dates
First available in Project Euclid: 13 March 2003

Permanent link to this document
https://projecteuclid.org/euclid.em/1047565645

Mathematical Reviews number (MathSciNet)
MR1418961

Zentralblatt MATH identifier
0864.51012

Subjects
Primary: 52C17: Packing and covering in $n$ dimensions [See also 05B40, 11H31]
Secondary: 65Y25

Citation

Conway, John H.; Hardin, Ronald H.; Sloane, Neil J. A. Packing lines, planes, etc.: packings in Grassmannian spaces. Experiment. Math. 5 (1996), no. 2, 139--159. https://projecteuclid.org/euclid.em/1047565645


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See also

  • See editors' note: Editors' note on "Packing lines, planes, etc.: packings in Grassmannian spaces". Experiment. Math. vol. 5, iss. 2, (1997), p.175.