Geodesic
The asymptotic number of set partitions with unequal block sizes
The electronic journal of combinatorics, Tome 6 (1999)
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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.
DOI : 10.37236/1434
Classification : 05A18, 05A16
Mots-clés : number of set partitions, generating function, coefficients, random partition 
@article{10_37236_1434,
     author = {A. Knopfmacher and A. M. Odlyzko and B. Pittel and L. B. Richmond and D. Stark and G. Szekeres and N. C. Wormald},
     title = {The asymptotic number of set partitions with unequal block sizes},
     journal = {The electronic journal of combinatorics},
     year = {1999},
     volume = {6},
     doi = {10.37236/1434},
     zbl = {0913.05008},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1434/}
}
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%A N. C. Wormald
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A. Knopfmacher; A. M. Odlyzko; B. Pittel; L. B. Richmond; D. Stark; G. Szekeres; N. C. Wormald. The asymptotic number of set partitions with unequal block sizes. The electronic journal of combinatorics, Tome 6 (1999). doi: 10.37236/1434

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