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:<math>\frac{g(z)^n}{|G|}.</math>
We are able to enumerate filled slot configurations using either PET in the unlabelled case or the labelled enumeration theorem in the labelled case. We now ask about the generating function of configurations obtained when there is more than one set of slots, with a permutation group acting on each. Clearly the orbits do not intersect and we may add the respective generating functions. Suppose, for example, that we want to enumerate unlabelled sequences of length two or three of some objects contained in a set ''X''. There are two sets of slots, the first one containing two slots, and the second one, three slots. The group acting on the first set is <math>E_2</math>, and on the second slot, <math>E_3</math>. We represent this by the following formal [[power series]] in ''X'':
:<math> X^2/E_2 \; + \; X^3/E_3 </math>
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