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Number of ways to distribute $n$ identical balls into $k$ identical boxes such that no box contains more than $m$ balls?
I wonder how to count the number of ways (algorithmically is fine) to distribute $n$ identical balls into $k$ identical boxes such that no box contains more than $m$ balls?
I've run into answers in ...
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0
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Relation of relative numbers of (restricted) ways to distribute identical / distinct objects into distinct bins
If want to know if the following inequality holds for general values of $s \leq n \ll m$.
$$\frac{C_0(n,m,s)}{C_0(n,m)} \leq \frac{p(n,m,s)}{m^n}$$
$C_0(n,m) = \binom{n+m-1}{m-1}$ is the number of ...
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