Geodesic
Random mappings with fixed elements
Matematičeskie voprosy kriptografii, Tome 2 (2011) no. 2, pp. 95-118 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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     title = {Random mappings with fixed elements},
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}
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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/

[1] Harris B., “Probability distributions related to random mappings”, Ann. Math. Statist., 31:4 (1960), 1045–1062 | DOI | MR | Zbl

[2] Cachkov V. N., “Otobrazheniya konechnogo mnozhestva s ogranicheniyami na kontury i vysotu”, Teoriya veroyatn. i ee primen., 17:4 (1972), 679–694 | MR | Zbl

[3] Sachkov V. N., Kombinatornye metody diskretnoi matematiki, Nauka, M., 1977

[4] Sachkov V. N., Veroyatnostnye metody v kombinatornom analize, Nauka, M., 1978 | MR | Zbl

[5] Riordan Dzh., Kombinatornye tozhdestva, Nauka, M., 1982 | MR | Zbl

[6] Feller V., Vvedenie v teoriyu veroyatnostei i ee prilozheniya, Mir, M., 1967 | Zbl

[7] Abel H., Oeuvres Completes, C. Groendahe, Christiania, 1839

[8] Kolchin V. F., Sluchainye otobrazheniya, Nauka, M., 1984 | MR | Zbl