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Two Integer Partition Problems

Let $P(n,k,m)$ be the number of partitions of $n$ into $k$ parts with all parts $\leq m$.

So $P(10,3,4) = 2$, i.e., (4,4,2); (4,3,3).

I need help proving the following:

$P(2n,3,n-1) = P(2n-3,3, n-2)$
$P(4n+3, 3, 2n+1) = P(4n,3,2n-1) + n + 1$.

1 Answers 1