@srivatsan: Here's the LaTeX code: This is related to my previous problem: http://math.stackexchange.com/q/82442/13425.
Let $a_{j,1}\ge a_{j,2}\ge \cdots \ge a_{j,n} \gt 0$, for $j=1,2,\ldots, k$, what is
$$\max_{\sigma_j\in S_n}\;\;\prod\limits_{i=1}^n\left(\sum\limits_{j=1}^k a_{j,\sigma_j(i)}\right)?$$
$S_n$ means the set of all the permuations on $\{1,\dots,n\}$.
Sn means the set of all the permuations on {1,…,n}.