I am studying the symbolic method and a question arose.
A construction is admissible if by associating a new class $\mathcal{C}=\Phi(\mathcal{A}_1,...,\mathcal{A}_j)$ , this implies that there is an operator Psi on generating functions, such that $C(x)=\Psi(A_1(x),.. .,A_j(x))$
For example, in the unlabeled world we have $\mathcal{C}=\text{Seq}(\mathcal{A})\to C(x)= \frac{1}{1-A(x)}$
My doubt is there are inadmissible constructions? Could someone give me an example of an inadmissible construction?