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The number of partitions of a set of N points in k dimensions induced by hyperplanes

Published online by Cambridge University Press:  20 January 2009

E. F. Harding
E. F. Harding
Affiliation:
Department of StatisticsUniversity of Edinburgh
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1. An arbitrary (k– 1)-dimensional hyperplane disconnects K-dimensional Euclidean space Ek into two disjoint half-spaces. If a set of N points in general position in Ek is given [nok +1 in a (k–1)-plane, no k in a (k–2)-plane, and so on], then the set is partitione into two subsets by the hyperplane, a point belonging to one or the other subset according to which half-space it belongs to; for this purpose the half-spaces are considered as an unordered pair.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 15 , Issue 4 , December 1967 , pp. 285 - 289
Copyright
Copyright © Edinburgh Mathematical Society 1967

References

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