Geodesic
Random mappings of finite sets with a known number of
Teoriâ veroâtnostej i ee primeneniâ, Tome 48 (2003) no. 4, pp. 818-828 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the class of all one-to-one mappings of an $n$-element set into itself, each of which has exactly $N$ connected components. Letting $n,N\to\infty$, we find that the asymptotic behavior of the mean and variance of the random variable is equal to the number of components of a given size in a mapping that is selected at random and is equiprobable among the elements of the mentioned class, and we prove the Poisson and local normal limit theorems for this random variable. Asymptotic estimates are found for the number of mappings with $N$ components, among which there are exactly $k$ components of a fixed size.
Keywords: random mapping, local limit theorem, asymptotic estimators, components. 
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A. N. Timashev. Random mappings of finite sets with a known number of. Teoriâ veroâtnostej i ee primeneniâ, Tome 48 (2003) no. 4, pp. 818-828. http://geodesic.mathdoc.fr/item/TVP_2003_48_4_a11/

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