The number of partitions of a set of N points in k dimensions induced by hyperplanes
The number of partitions of a set of N points in k dimensions induced by hyperplanes
复制标题
由超平面引起的 k 维中的 N 个点集的分区数
DOI：
10.1017/s0013091500011925
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发表时间：
1967
影响因子：
0.7
通讯作者：
E. Harding
中科院分区：
文献类型：
--
作者：
E. Harding
1.一个任意的（k- 1）维超平面将K维欧氏空间Ek断开成两个不相交的半空间。如果给定一个在Ek中一般位置的N个点的集合[在（k-1）-平面中nok +1，在（k-2）-平面中没有k，等等]，那么这个集合被超平面分成两个子集，一个点属于一个子集或另一个子集取决于它属于哪个半空间;为此目的，半空间被认为是无序对。
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.