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Solution of a research problem

Solution of a research problem In this paper, we solve the following research problem. LetX be a finite set andP the collection of all nonempty proper subsets ofX. A subsetT ofP is called a tree of subsets ofX ifA,B∈T implies thatA∩B∈{∅,A,B}. LetN[n,k] denote the number of allk-member trees of subsets of ann-element set. We deduce a recurrence equation onN[n,k], and give an analytic formula ofN[n,k]. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Solution of a research problem

Acta Mathematicae Applicatae Sinica , Volume 12 (3) – Jul 14, 2005

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Publisher
Springer Journals
Copyright
Copyright © 1996 by Science Press, Beijing, China and Allerton Press, Inc., New York, U.S.A.
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/BF02011894
Publisher site
See Article on Publisher Site

Abstract

In this paper, we solve the following research problem. LetX be a finite set andP the collection of all nonempty proper subsets ofX. A subsetT ofP is called a tree of subsets ofX ifA,B∈T implies thatA∩B∈{∅,A,B}. LetN[n,k] denote the number of allk-member trees of subsets of ann-element set. We deduce a recurrence equation onN[n,k], and give an analytic formula ofN[n,k].

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jul 14, 2005

References