A Metrization for Power-Sets with Applications to Combinatorial Analysis
A Metrization for Power-Sets with Applications to Combinatorial Analysis
复制标题
幂集的度量及其在组合分析中的应用
DOI：
10.4153/cjm-1960-014-0
复制
发表时间：
1960
期刊：
影响因子：
--
通讯作者：
R. Silverman
中科院分区：
文献类型：
--
作者：
R. Silverman
组合配置通常可以根据受某些条件约束的对象到集合中的布置来措辞。有鉴于此，问题就产生了：给定一个集合S和它的幂集Us（S的所有子集的类），是否有可能以组合上有意义的方式来构造Us。本文提出并研究了一个这样的结构，通过定义一个距离函数超过美国。给定A，B在Us中，定义它们的距离，其中N（E）表示E中元素的数量，+ ∞是一个容许值。
Combinatorial configurations may generally be phrased in terms of arrangements of objects into sets subject to certain conditions. In view of this, the question arises as to whether given a set S and its power-set Us (the class of all subsets of S), it might be possible to structure Us in a combinatorially significant manner. This paper proposes and investigates one such structuring achieved by defining a distance function over US. Given A, B in Us , define their distance by where N(E) denotes the number of elements in E, + ∞ being an admissible value.