一句话：通过孤立子序的商构造建立闭包数量关系，并给出递归计数闭包算子的方法。
本文研究孤立子序与闭包算子之间的相互作用。孤立子序是一类特殊子序，能够通过商构造减少有序集的元素数量。作者指出，原有序集与由孤立子序诱导的商有序集之间，其闭包数量存在简单公式联系。基于这些联系，论文说明当给定有序集包含合适的孤立子序时，可以导出递归算法来计数闭包算子。该工作将序结构分解与闭包计数联系起来，为闭包算子的枚举提供了一种可递归应用的理论方法。摘要未报告实现或实验，属于理论性研究。
In this paper we investigate the interplay between isolated suborders and closures. Isolated suborders are a special kind of suborders and can be used to diminish the number of elements of an ordered set by means of a quotient construction. The decisive point is that there are simple formulae establishing relationships between the number of closures in the original ordered set and the quotient thereof induced by isolated suborders. We show how these connections can be used to derive a recursive algorithm for counting closures, provided the ordered set under consideration contains suitable isolated suborders.