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{\bf A. Knopfmacher, A. M. Odlyzko, B. Pittel, L. B. Richmond, D. Stark, G. Szekeres and N. C. Wormald}
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{\bf The Asymptotic Number of Set Partitions with Unequal Block Sizes}
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The asymptotic behavior of the number of set partitions of an $n$-element
set into blocks of distinct sizes is determined.
This behavior is more complicated than is typical for set partition
problems.
Although there is a simple generating function, the usual analytic methods for
estimating coefficients fail in the direct approach,
and elementary approaches combined with some analytic methods are used to
obtain
 most of the results.
Simultaneously, we obtain results on the shape of a random partition of an
$n$-element
set into blocks of distinct sizes.



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