Definition. The permanent of an n-by-n matrix A = (a i,j) is defined as = ∑ ∈ ∏ =, (). The sum here extends over all elements σ of the symmetric group S n; i.e. over all permutations of the numbers 1, 2, ..., n.. For example, = +, and = + + + + +. The definition of the permanent of A differs from that of the determinant of A in that the signatures of the permutations are not ...
