On a combinatorial problem related to permanents (Q1109771)

For a square matrices, the permanent is the sum of all products with exactly one element from each row and each column. With \(n\times n\) elements we can form \((n^ 2)!2(n!)^ 2\) different permanents. The author studies the following problem: Find matrix configurations of the member \(1,2,...,n^ 2\) which make the permanent maximum and minimum. Some numerical results for \(n=1,...,8\) are presented.