 Generating function for partitions with bounded parts

ID: generating-function-for-partitions-with-bounded-parts

The generating function for partitions whose parts are at most

e

\prod_{i = 1}^{e} \frac{1}{1 - x ^{i}} .

Conjugating Young diagrams shows that it also counts partitions with at most

e

x^{e}

gives the generating function for partitions with exactly

e

positive parts.

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