Consider the symmetrization of tensor product $t_i\otimes t_j\otimes t_k$, i.e. $Sym^3(S)$, where $S=t_i$, can we say $t_1^2t_2\oplus t_2t_1^2$ is symmetrized (when n>=4)? or should we write it as "$t_1^2t_2\oplus t_2^2t_1$"? I'd prefer the later one, but someone told me the previous one, $t_1^2t_2\oplus t_2t_1^2$, is also rightly symmetrized.
This confused me.