偏序关系中盖住集的判定

Judgement of Covering Assembly in Partially Ordered Relation

直接根据现有离散数学教材中偏序关系中“盖住”的定义,来判定偏序关系中的盖住集,有时比较困难。文中通过对教材中偏序关系中“盖住”定义的深入分析,将定义“对于任意a,b∈A,当<a,b>∈R,a≠b且没有其它元素c满足<a,c>∈R和<c,b>∈R,则称元素b盖住元素a,并且记COVR={<a,b>|a,b∈A;b盖住a}”改为“对于任意<a,b>∈R且a=b,则<a,b>∈IR,令R1=R-IR,则R1-(R1○R1)为盖住集”,得出一种等价的定义形式。利用该等价定义可以较好地实现盖住集的判定。

There is a bit difficult in judging covering assembly in partially ordered relation on a basis of its definition in discrete mathematic. Here gives an equivalent definition,by replacing＂ 对于任意对于任意a,b∈A,当〈a,b〉∈R,a≠b且没有其它元素c满足〈a,c〉∈R和〈c,b〉∈R则称元素b盖住元素a,并且记ODVR={〈a,b〉｜a,b∈A;b盖住a}＂with＂对于任意〈a,b〉∈RRa=b,则〈a,b〉∈IR,令R1=R-IR,则R1-（R1OR1）为盖住集＂ With this equivalent definition, it is easier to judge covering ascmbly in partially ordered relation.