Intrinsic permutation symmetry of nonlinear susceptibility

Commuting input field factors permit the response kernel to be symmetrized under interchange of input index-frequency pairs. For example ${\chi }_{ijk}^{(2)}({\omega }_s;{\omega }_1,{\omega }_2)={\chi }_{ikj}^{(2)}({\omega }_s;{\omega }_2,{\omega }_1)$. This does not authorize exchanging indices while keeping unequal frequency arguments in their old slots, nor exchanging the output index without further assumptions.