分类集及极大分类集的计数

The Enumeration of Taxonomic and Maximal Taxonomic Classes of Sets

Ｍ是（１，２，…，ｎ）的一些子集合的集合。若Ｍ中任意两个子集，或者它们无共同元素，或者一个是另一个的子集，这样的Ｍ称为分类集。若不存在（１，２，…，ｎ）的一个分类集包含Ｍ，称Ｍ为极大分类集。给出分类集及极大分类集个数ｔｎ及Ｔｎ的计算，并由Ｔｎ的两个递推关系式得到一些组合恒等式。

Let M be a set whose elements are subsets of In= {1,2, ..., n} .M is called taxonomic class of sets if. for every two elements of M, either they are disjoint, or one is a subset of the other. M is maximal if no other taxonomic class of sets contains it. The numbers t., T. of taxonomic and maximal taxonomic classes of sets are given. From the two given recurrence relations of Tn, several combinatorial identities are obtained.