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Another example (and a classic combinatorics problem) is [[integer partition]]s. First, define the class of positive integers <math>\mathcal{I}</math>, where the size of each integer is its value:
:<math>\mathcal{I} = \mathcal{Z} \times \mathfrak{G}\{\mathcal{Z}\}
The OGF of <math>\mathcal{I}</math> is then
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Now, define the set of partitions <math>\mathcal{P}</math> as
:<math>\mathcal{P} = \mathfrak{M}\{\mathcal{I}\}. </math>
The OGF of <math>\mathcal{P}</math> is
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