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2 votes

Which unordered partition of $n$ gives rise to the largest number of ordered partitions?

Some heuristic way to the answer, related to well-known properties of the entropy of probability distributions, is loosely as follows. Set $m=\sum_i a_i$ and $p_i=a_i/m$, so that $p=(p_i)_{i\ge1}$ is …
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