A. N. Timashov
Random partitions of a set with given number of blocks
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 → ∞, 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.
Discrete Mathematics and Applications, Walter de Gruyter
Print ISSN: 0924-9266
Volume: 13, 07/2003
Pages: 307 - 317
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