I'm trying to decide which of the following are alternating tensors in $\mathbb R^4$ and express those that are in terms of the elementary tensors on R^4:
$f(x,y) = x_1y_2 = x_2y_1 + x_1y_1$ \begin{align*} g(x, y) &= x_1y_3 - x_3y_2 \\ h(x, y) &= x_1^3y_2^3 - x_2^3y_1^3 \end{align*}
All I can tell is that we have to define a $\sigma$ permutation by $f(\sigma(x),\sigma(y) =$
and I'm trying to go about solving it.