Published online by Cambridge University Press: 20 January 2009
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.