\mathop = \limits^{{\rm per}\left( I \right) = J} M\left( {e^{i_1 } ,...,e^{i_k } } \right)\left( { - 1} \right)^{\sigma \left( {{\rm per}} \right)} \underbrace {dx_{{\rm per}\left( I \right)} \left( {e^{j_1 } ,...,e^{j_k } } \right)}_{ = 1} =