Enumeration of Closed Family of Finite Sets

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Enumeration of Closed Family of Finite Sets

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- Enumeration of Closed Family of Finite Sets
- Acta Scientiarum Naturalium Universitatis SunYatseni Vol. 49, Issue 6, Pages: 11-14(2010)
- 作者机构：
  
  1. 天水师范学院数学与统计学院,甘肃,天水,741001
  2. 
- 作者简介：
- 基金信息：
- DOI：
  CLC：
- Published：2010，
  
  Published Online：25 November 2010，
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Enumeration of Closed Family of Finite Sets. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 49(6):11-14(2010)
DOI：

Enumeration of Closed Family of Finite Sets. [J]. Acta Scientiarum Naturalium Universitatis SunYatseni 49(6):11-14(2010) DOI：

摘要

设集合X={a

…

}

f(n

m)表示X的含m个元素的不同封闭集族的数目。证明了f(n

m)=({3

-2

m=24

-2·3

m=35

-5∕2·4

+2·3

-2

n-1



m=4; 其中n=1

…。6

-3·5

+3·4

-3

m=5.

Abstract

Let X={a

…

} be a finite set and f(n

m) the number of closed family of sets with

elements of

. Then we show that: For every integer n≥1

f(n

m)=({3

-2

m=24

-2·3

m=35

-5∕2·4

+2·3

-2

n-1



m=46

-3·5

+3·4

-3

m=5.

关键词

子集幂集封闭集族

Keywords

subsetpower setclosed family of sets

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