Fubini定理公式数计数和φ(n,k)卷积公式

The Counting Formula of Fubini Theorm' s Formula Number and The Formula Convolutions of φ(n,k)

组合数学中,Catalan数有显式公式,Fibini定理公式数无显式公式,本文利用完全图Kn的k个分支的完全分支覆盖的个数N(Knk)=S(n,k)(第二类Stirling数)和卷积公式,作者将导出Fibini定理的公式数的显式公式,此外获得完全i-部图所有个数计数公式,本文中提出φ(n,k)概念,并讨论φ(n,k)的组合卷积公式,最后证明φ(n)=sumfork=1ton(1/k)φ(n,k)与Fibini公式数之间的关系等式。

For combinatoria, there was the explicit formula of Catalan number, so far we haven't been the explicit formula of Fibini theorem's formula number, in this paper, by means of the equality N(Kn,k) = S(n,k) (the Stirling number of the second kind) and the formula convolution, the author derives the explicit formula of Fibini theorem s formula number, gains the cardinal formula of the number of all complete i - partite graphs, suggests the definition of φ(n,k) , as well as discusses the formula convolutions of φ(n,k) , finally the relation formu la between φ(n) = sun from k-1 to n(1/k)φ(n,k) and the Fibini number is proved.