| SOLUTION OF A RESEARCH PROBLEM |
| |
| 作者姓名： | 巫世权 |
| |
| 作者单位： | Department of Mathematics，National University of Technology，Changsha 410073，China |
| |
| 摘 要： | ＳＯＬＵＴＩＯＮＯＦＡＲＥＳＥＡＲＣＨＰＲＯＢＬＥＭＷＵＳＨＩＱＵＡＮ（巫世权）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＮａｔｉｏｎａｌＵｎｉｖｅｒｓｉｔｙｏｆＴｅｃｈｎｏｌｏｇｙ，Ｃｈａｎｇｓｈａ４１００７３，Ｃｈｉｎａ）Ａｂｓｔｒａｃｔ...
|
| 收稿时间： | 10 March 1993 |
Solution of a research problem |
| |
| Shiquan Wu.SOLUTION OF A RESEARCH PROBLEM[J].Acta Mathematicae Applicatae Sinica,1996,12(3):289-299. |
| |
| Authors: | Shiquan Wu |
| |
| Institution: | (1) Department of Mathematics, National University of Technology, 410073 Changsha, China |
| |
| Abstract: | In this paper, we solve the following research problem. Let X be a finite set and P the collection of all nonempty proper subsets of X. A subset T of P is called a tree of subsets of X if A,BT implies that AB{,A,B}. Let Nn,k] denote the number Of all k-member trees of subsets of an n-element set. We deduce a recurrence equation on Nn,k], and give an analytic formula of Nn,k].With the application of Nn,k], the open problem is settled. The maximum trees of subsets of an n-set are also studied. |
| |
| Keywords: | Tree of subsets number of tree of subsets maximum tree of subsets |
| 本文献已被 CNKI SpringerLink 等数据库收录！ |
