有限集合的相容关系与完全覆盖  

Compatibility Relations and Complete Cover of Finite Sets

作　　者：冯淑霞[1,2] 王洁[3] 董道珍[3] 

机构地区：[1]河南大学现代数学研究所,河南开封475004 [2]河南大学数学与信息科学学院,河南开封475004 [3]商丘工学院基础部,河南商丘476000

出　　处：《河南大学学报（自然科学版）》2011年第5期441-446,共6页Journal of Henan University:Natural Science

基　　金：国家自然科学基金资助项目(11001074);河南省高等学校青年骨干教师资助计划项目

摘　　要：非空有限集合A的完全覆盖S={A1,A2,…,An}决定了A上的相容关系R=∪ni=1(Ai×Ai).研究了R的最大相容类集合和完全覆盖S之间的关系,给出相容的完全覆盖、极大相容完全覆盖、极小相容完全覆盖和恰当完全覆盖的定义,证明了相容的完全覆盖其成员均为R的最大相容类,而极大相容完全覆盖恰为R的最大相容类的全体,并给出这几种完全覆盖之间的关系.The complete cover S={A1,A2,…,An} of a finite set A decides the compatibility relation R=∪ni=1（Ai×Ai） on the set A.This paper is designed to research the relationship between all the maximal compatibility classes decided by R and the complete cover.So the definition of a compatible complete cover,a maximal compatible complete cover,a minimal compatible complete cover,and an appropriate complete cover are given in the paper.It proves that every element of the compatible complete cover is the maximal compatibility class and the maximal compatible complete cover is just all the maximal compatibility classes decided by R,and analyses the relations of complete covers of these different classes.

关 键 词：相容关系 完全覆盖 极大相容完全覆盖 最大相容类 

分 类 号：O144.1[理学—数学]