Matrix Permanent

Let A=(a_{ij}) be an n by n real matrix. The permanent of A is defined as
\[
per(A)=
sum_{\sigma} a_{1,sigma(1)}a_{2,sigma(2)}...a_{n,sigma(n)}
\]
where the sum runs through all the possible permutation \sigma on the set {1,2,...,n}, and \sigma(i) stands for the image of the number i under \sigma.
The routine deals with computation of permanent a square matrix. The permanent of a matrix is very important in many fields especially in combinatorics, where it is used to charaterize configurations of a system or the structure of a graph.

[1] R.A.Brauldi, Introductory Combinatorics, Fourth Edition, Pearson Education.