We define the following subgroups of the automorphism group of $k[x_1, \ldots, x_n]$
E(k,n) is the subgroup generated by elementary $k$-automorphisms of $k[x_1, \cdots, x_n]$ of the form $(x_1, x_2, \cdots, x_{i-1}, x_i + a, x_{i+1}, \cdots, x_n)$ where $a \in k[x_1,x_2, \cdots, x_{i-1},x_{i+1}, \cdots, x_n]$
Aff(k,n) is the subgroup of linear transformations
J(k,n) is the subgroup generated by elementary $k$-automorphisms of $k[x_1, \cdots, x_n]$ of the form $(x_1, x_2 + f_2, x_3 + f_3, \cdots, x_n+f_n)$ where $f_i \in k[x_1, \cdots, x_{i-1}]$ for $2 \leq i \leq n$.
I've been having trouble figuring out a way to write an element of E(k,n) as a composition of linear transformations and elements of J(k,n). I know it involves some permutation of the $x_i$s.
Any help would be appreciated. Thanks.