ABSTRACT
Thus, under the condition that the susceptibilities are real (all frequencies far from any resonance), the susceptibilities are unchanged for the simultaneous permutation of subscripts from the cartesian set {ijkl} and the corresponding subscripts from the frequency set {4123}, with the stipulation that the frequencies carry the proper sign. Note: The first frequency in the argument, that is, the generated frequency, carries a negative sign. The signs on the other frequencies must be such that the algebraic sum of all frequencies is zero. For example, –w4 + w3 + w2 + w1 = 0 implies that –w2 – w1 + w4 – w3 = 0. This is called full permutation symmetry. This symmetry generalizes to all orders.
