The generalized determinant and its application to the enumeration of permutations

In this work we present a method of enumeration of restricted permutations belonging to two arbitrary disjoint complementary classes. This method is based on combinatorial properties of the generalized determinant and the permanent. In particular, we apply this method to enumeration of restricted permutations with special character of inversions. We also show the connection between the generalized determinant and associative finite dimensional algebras with nilpotent generators.