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On partitions of N points

Published online by Cambridge University Press:  20 January 2009

Donald Watson
Donald Watson
Affiliation:
RAAF Academy, Point CookAustralia
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In a paper (1) by Harding there is a tacit invitation to seek the connection between the following two problems:

(i) Find the number, ηk(N), of regions into which a k-dimensional space is partitioned by a set of N (k- l)-dimensional hyperplanes.

(ii) Find the number, vk(N), of distinct partitions of a given set of N points in a k-dimensional space E that can be induced by (k- 1)-dimensional hyperplanes.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 16 , Issue 3 , June 1969 , pp. 263 - 264
Copyright
Copyright © Edinburgh Mathematical Society 1969

References

REFERENCES

(1)Harding, E. F.The number of partitions of a set of N points in k dimensions by hyperplanes, Proc. Edinburgh Math. Soc. (2) 15 (1967), 285–289.CrossRefGoogle Scholar
(2)Schläfli, L.Theorie der vielfachen Kontinuität (Berne (1852); Ges. Math. Abh. I (Basel, 1950), p. 209).Google Scholar