Random substitutions with transformed cycles
Matematičeskie voprosy kriptografii, Tome 3 (2012), pp. 127-150.

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Let for the cycles of a random substitution two types of transformations are defined: deterministic and stochastic. We obtain exact and asymptotic distributions for the numbers of nontransformed cycles and $r$-cycles, for the cardinalities of the transitivity domains defined by such cycles.
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V. N. Sachkov. Random substitutions with transformed cycles. Matematičeskie voprosy kriptografii, Tome 3 (2012), pp. 127-150. http://geodesic.mathdoc.fr/item/MVK_2012_3_a5/

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