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===Multiset===
The ''multiset construction'', denoted <math>\mathcal{A} = \mathfrak{M}\{\mathcal{B}\}</math> is a generalization of the set construction. In the set construction, each element can occur zero or one times. In a multiset, each element can appear an arbitrary number of times. Therefore,
:<math>\mathfrak{M}\{\mathcal{B}\} = \prod_{\beta \in \mathcal{B}} \mathfrak{G}\{\beta\}.</math>
This leads to the relation
:<math>\begin{align} A(z) &{} = \prod_{\beta \in \mathcal{B}} (1 - z^{|\beta|})^{-1} \\
&{} = \prod_{n = 1}^{\infty} (1 - z^{n})^{-B_{n}} \\
&{} = \exp \left ( \ln \prod_{n = 1}^{\infty} (1 - z^{n})^{-B_{n}} \right ) \\
&{} = \exp \left ( \sum_{n=1}^{\infty}-B_{n} \ln (1 - z^{n}) \right ) \\
&{} = \exp \left ( \sum_{k=1}^{\infty} \frac{B(z^{k})}{k} \right ),
\end{align}
</math>
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