where $\sum_\pi$ is the sum over argument-permutations, e.g.

$\sum_\pi\ g(a,b,c)\equiv g(a,b,c)+g(c,a,b)+g(b,c,a)+g(a,c,b)+g(b,a,c)+g(c,b,a)$.

Relevant for discussions of kinetics on the intermediate level $f_1$ and $f_2$. And maybe $f_3$ if you're mad enough.

Notice that if $\bar f_s$ is already a symmetric function, $f_s=\bar f_s$.

Reduced distribution function