Tagged Questions
3
votes
1answer
102 views
An inequality involving Stirling numbers of the second kind
The task is to prove the following inequality:
$\begin{Bmatrix} mn\\ n \end{Bmatrix} \geqslant \frac{(mn)!}{(m!)^nn!}$ , where $m, n \in \mathbb{N_+}$
and to determine when the equality ...
0
votes
0answers
208 views
Inequality with Stirling's numbers
I supect that for all $n>k>0$:
$k^2\left\{ \begin{array}{c}n\\k\end{array} \right\}^2 +2k\left\{ \begin{array}{c}n\\k\end{array} \right\}\left\{ \begin{array}{c}n\\k-1\end{array} ...
1
vote
0answers
89 views
Inequality with Stirling's numbers of the second kind [duplicate]
Possible Duplicate:
Proof strategy - Stirling numbers formula
Prove inequality:
$ \left\{\begin{array}{c}n\\k-1\end{array}\right\}\left\{\begin{array}{c}n\\k+1\end{array}\right\} \le ...
