Geodesic
Random substitutions with cycles of bounded lengths and transforming
Matematičeskie voprosy kriptografii, Tome 5 (2014) no. 3, pp. 117-136 
V. N. Sachkov. Random substitutions with cycles of bounded lengths and transforming. Matematičeskie voprosy kriptografii, Tome 5 (2014) no. 3, pp. 117-136. http://geodesic.mathdoc.fr/item/MVK_2014_5_3_a5/
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     title = {Random substitutions with cycles of bounded lengths and transforming},
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Voir la notice de l'article provenant de la source Math-Net.Ru

Random substitutions of degree $n$ having the uniform distribution on the set of substitutions with cycles lengths belonging to the set $A\subseteq\{1,2,\dots,m\}$ are considered. Cycles of such substitution are transformed independently with probabilities depending on the cycle length. Exact and limits distributions of the number of nontransformed cycles are investigated.

[1] Mozer L., Wyman M., “An asymptotics for the Bell numbers”, Trans. Roy. Soc. Canada. Sec. 3, 49 (1955), 49–54 | MR

[2] Curtiss J. N., “A note on the theory of moment generating functions”, Ann. Math. Statist., 13:3 (1942), 430–433 | DOI | MR | Zbl

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

[4] Sachkov V. N., Probabilistic methods in combinatorial analysis, Encyclopedia of Mathematics and its Applications, 56, Cambridge Univ. Press, 1997 | MR | Zbl

[5] Flajolet P., Sedgewick R., Analytic Combinatorics, Cambridge Univ. Press, 2009 | MR | Zbl

[6] Sachkov V. N., “Sluchainye podstanovki s transformirovannymi tsiklami”, Matematicheskie voprosy kriptografii, 3:4 (2012), 127–150