Let $(\mathcal{A}_n)_{n\geq 0}$ and $(\mathcal{B}_n)_{n\geq 0}$ be sequences of finite sets such that the sets $\mathcal{A}_n$ are pairwise disjoint and the sets $\mathcal{B}_n$ are pairwise disjoint. Define the underlying graded classes by
be the product graded class with graded pieces $(\mathcal{C}_n)_{n\geq 0}$. Define the ordinary generating functions $A(X),B(X),C(X)\in \mathbb{Z}[[X]]$ by