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Results tagged with partitions
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user 15428
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The number of partitions of a positive integer allowing at most r repetitions of any part
Let $q_r(n)$ be the number of partitions of the positive integer $n$ allowing at most $r$ repetitions of any of the parts. … (For $r=1$ this is just the usual number of partitions of $n$ into distinct parts.) For $n = 5$ and $r = 2$ these partitions are precisely
5,
4 + 1,
3 + 2,
3 + 1 + 1, and
2 + 2 + 1.
So $q_2(5) = 5$. …
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