Out of curiosity, I checked the permanent of an antisymmetric matrix. The permanent has the same expansion into n! terms as the determinant, except that the coefficient is always +1 rather than the sign of the permutation. For an odd order antisymmetric matrix, the permanent vanishes, for the same reason as the determinant. For an even order antisymmetric matrix, I factored the order 4, 6, and 8 permanents using Maple. They do not factor. Gene