Geodesic
On one characteristic of a random mapping with given number of cycles
Diskretnaya Matematika, Tome 18 (2006) no. 3, pp. 43-60
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We consider the random variable equal to the number of trees of given size in the graph of a random one-to-one mapping of an $n$-element set into itself with $m$ connected components. We obtain limit theorems which describe the distribution of this characteristic in the case where $n\to\infty$, $m/\ln n\to\infty$, $m/\ln n=O(\ln n)$. 
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I. A. Cheplyukova. On one characteristic of a random mapping with given number of cycles. Diskretnaya Matematika, Tome 18 (2006) no. 3, pp. 43-60. http://geodesic.mathdoc.fr/item/DM_2006_18_3_a2/

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