Exercise 1, § 2

We adopt the notation $T, J, T_n$ of Definition 1 and no. 6. Let $t$ be a homogeneous tensor of $T$ of order $p$ and $\sigma$ a permutation of $\{1, 2, \ldots, p\}$. Then $t - \sigma t \in J + T_{p-1}$. (Reduce it to the case where $\sigma$ is a transposition of two consecutive integers.)