 The "immanant" of an formula_5 matrix formula_6 associated with the character formula_3 is defined as the expression

The determinant is a special case of the immanant, where formula_3 is the alternating character formula_10, of "S""n", defined by the parity of a permutation.The permanent is the case where formula_3 is the trivial character, which is identically equal to 1.For example, for formula_12 matrices, there are three irreducible representations of formula_13, as shown in the character table