Geodesic
Distribution of the number of nonappearing lengths of cycles in a~random mapping
Matematičeskie zametki, Tome 23 (1978) no. 6, pp. 895-898

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One-to-one random mappings of the set $\{1,2,\dots,n\}$ onto itself are considered. Limit theorems are proved for the quantities $\mu_i$, $0\le i\le n$, $\max\limits_{0\le i\le n}\mu_i$, $\min\limits_{0\le i\le n}\mu_i$, where $\mu_i$ is the number of 0leilen components of the vector ($\alpha_1,\alpha_2,\dots,\alpha_n$) which are equal to $i$, $0\le i\le n$ and $\alpha_r$ is the number of components of dimension $r$ of the random mapping. 
@article{MZM_1978_23_6_a12,
     author = {A. S. Ambrosimov},
     title = {Distribution of the number of nonappearing lengths of cycles in a~random mapping},
     journal = {Matemati\v{c}eskie zametki},
     pages = {895--898},
     publisher = {mathdoc},
     volume = {23},
     number = {6},
     year = {1978},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1978_23_6_a12/}
}
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A. S. Ambrosimov. Distribution of the number of nonappearing lengths of cycles in a~random mapping. Matematičeskie zametki, Tome 23 (1978) no. 6, pp. 895-898. http://geodesic.mathdoc.fr/item/MZM_1978_23_6_a12/