3
votes
1answer
131 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 ...
1
vote
0answers
232 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
91 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 ...