Geodesic
Random partitions of sets with a known number of blocks
Diskretnaya Matematika, Tome 15 (2003) no. 2, pp. 138-148

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We consider the class of all partitions of a set of $n$ elements into $N$ blocks. Provided that the uniform distribution is given on this class and $n,N\to\infty$, we describe the asymptotic behaviour of the mathematical expectation and variance and prove Poisson and local normal limit theorems for the random variable equal to the number of blocks of a given size in a partition chosen at random. We find asymptotic expansions of the number of partitions of a set of $n$ elements into $N$ blocks with exactly $k=k(n,N)$ blocks of a given size. 
@article{DM_2003_15_2_a11,
     author = {A. N. Timashev},
     title = {Random partitions of sets with a known number of blocks},
     journal = {Diskretnaya Matematika},
     pages = {138--148},
     publisher = {mathdoc},
     volume = {15},
     number = {2},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2003_15_2_a11/}
}
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A. N. Timashev. Random partitions of sets with a known number of blocks. Diskretnaya Matematika, Tome 15 (2003) no. 2, pp. 138-148. http://geodesic.mathdoc.fr/item/DM_2003_15_2_a11/