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Is there accepted notation for the set of ways of partitioning a natural number $a$ into $b$ parts?
Recall the following:
Multinomial Theorem. For all finite sets $X$, we have:
$$\left(\sum_{x \in X} x\right)^n = \sum_{a}[a](X)^a$$
where $a$ ranges over the set of partitions of $n$ into ...
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