Geodesic
A case of the limit distribution of the number of cyclic vertices in a random mapping
Diskretnaya Matematika, Tome 16 (2004) no. 3, pp. 76-84

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We consider the number of cyclic vertices in a random single-valued mapping of a set of size $n$ whose graph contains $m$ cycles. We obtain a theorem that describes the limit behaviour of this characteristic as $n\to\infty$, $m/\ln n\to\infty$, $m/\ln n=O(\ln n)$.This research was supported by grant 1758.2003.1 of the President of Russian Federation for support of the leading scientific schools. 
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     author = {I. A. Cheplyukova},
     title = {A case of the limit distribution of the number of cyclic vertices in a random mapping},
     journal = {Diskretnaya Matematika},
     pages = {76--84},
     publisher = {mathdoc},
     volume = {16},
     number = {3},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2004_16_3_a3/}
}
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I. A. Cheplyukova. A case of the limit distribution of the number of cyclic vertices in a random mapping. Diskretnaya Matematika, Tome 16 (2004) no. 3, pp. 76-84. http://geodesic.mathdoc.fr/item/DM_2004_16_3_a3/