Geodesic
Random mappings with fixed elements
Matematičeskie voprosy kriptografii, Tome 2 (2011) no. 2, pp. 95-118 
V. N. Sachkov. Random mappings with fixed elements. Matematičeskie voprosy kriptografii, Tome 2 (2011) no. 2, pp. 95-118. http://geodesic.mathdoc.fr/item/MVK_2011_2_2_a4/
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     author = {V. N. Sachkov},
     title = {Random mappings with fixed elements},
     journal = {Matemati\v{c}eskie voprosy kriptografii},
     pages = {95--118},
     year = {2011},
     volume = {2},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MVK_2011_2_2_a4/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

We consider orgraphs of random mappings of $n$-element set having uniform distribution on the set of all mappings with fixed points. Formulas for exact and limit distributions of the number of vertices in a tree or in a forest containing a given vertex are derived along with analogous results for the height of a given vertex conditioned to belong to a forest. Exact and limit distributions of the height of a given vertex in a random rooted tree or forest with $n$ vertices are derived also.

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