permanent

In linear algebra, the permanent of a square matrix is a function of the matrix similar to the determinant. The permanent, as well as the determinant, is a polynomial in the entries of the matrix. Both are special cases of a more general function of a matrix called the immanant. Definition The permanent of an matrix is defined as The sum here extends over all elements σ of the symmetric group Sn; i.e. over all permutations of the numbers 1, 2, ..., n. For example,