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Random partitions of a set with given number of blocks
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A. N. Timashov
Published/Copyright:
July 1, 2003
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.
Published Online: 2003-07-01
Published in Print: 2003-07-01
Copyright 2003, Walter de Gruyter
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Articles in the same Issue
- Independent systems of automata in labyrinths
- Estimation of the time needed to set up a covert channel
- Schemes of public distribution of keys based on a non-commutative group
- Characteristic polynomials of multi-index transportation problems
- Construction of maximally non-Hamiltonian graphs
- Generating triples of involutions of large sporadic groups
- On the number of reversible homogeneous structures
- Random partitions of a set with given number of blocks
- On two statistics of chi-square type based on frequencies of tuples of states of a high-order Markov chain
