Pattern inventory
= Pattern inventory
{title2=$F_G(x)=\sum_{\text{coloring orbits}}\prod_{s\in S}x_{f(s)}$}
This is the sum of content <monomials> of colorings up to the <group action>. It equals the <cycle index> specialized at $t_r=p_r(x)$. One may first use finitely many colors; stabilization defines the corresponding homogeneous <symmetric function>. Calling the specialized cycle index a cycle indicator makes $Z_G=F_G$ an equality in the same variables.