Applications of an inequality in information theory to matrices (Q1072614)

The author proves inequalities such as \(per_ KZ\geq per_ KA\prod_{i,j}(z_{ij}/a_{ij})^ bij\) where \(per_ K\) is the sum of all diagonal products over an arbitrary set of permutations, Z, A are any nonnegative matrices with \(per_ KA\) positive, and B is \(b_{ij}=a_{ij}per A(i,j)/per A\).