Compatibility Relations and Complete Cover of Finite Sets
Dong Dao-zhen · Journal of Henan University · 2011
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.