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Mat. Vopr. Kriptogr., 2018, Volume 9, Issue 3, Pages 99–108 (Mi mvk264)  

This article is cited in 5 scientific papers (total in 5 papers)

On the sets of images of $k$-fold iteration of uniform random mapping

V. O. Mironkina, V. G. Mikhailovb

a National Research University Higher School of Economics, Moscow
b Steklov Mathematical Institute of RAS, Moscow

Abstract: The properties of the graph of $k$-fold iteration of uniform random mapping $f\colon \{1,\ldots,n\}\to \{1,\ldots,n\}$ are studied. Some recurrence formulas for the probabilities for a vertex to belong to the set of images $f^k(\{1,\ldots,n\})$ and to the set of the initial vertices in the graph of $f^k$ are obtained.

Key words: uniform random mapping, iteration of random mapping, graph of a mapping, image, pre-image, initial vertex.

DOI: https://doi.org/10.4213/mvk264

Full text: PDF file (201 kB)
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UDC: 519.212.2+519.719.2
Received 11.V.2017, 05.VI.2018

Citation: V. O. Mironkin, V. G. Mikhailov, “On the sets of images of $k$-fold iteration of uniform random mapping”, Mat. Vopr. Kriptogr., 9:3 (2018), 99–108

Citation in format AMSBIB
\Bibitem{MirMik18}
\by V.~O.~Mironkin, V.~G.~Mikhailov
\paper On the sets of images of $k$-fold iteration of uniform random mapping
\jour Mat. Vopr. Kriptogr.
\yr 2018
\vol 9
\issue 3
\pages 99--108
\mathnet{http://mi.mathnet.ru/mvk264}
\crossref{https://doi.org/10.4213/mvk264}
\elib{https://elibrary.ru/item.asp?id=35601224}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. O. Mironkin, “Ob otsenkakh raspredeleniya dliny otrezka aperiodichnosti v grafe $k$-kratnoi iteratsii ravnoveroyatnogo sluchainogo otobrazheniya”, PDM, 2018, no. 42, 6–17  mathnet  crossref  elib
    2. V. O. Mironkin, “Sloi v grafe $k$-kratnoi iteratsii ravnoveroyatnogo sluchainogo otobrazheniya”, Matem. vopr. kriptogr., 10:1 (2019), 73–82  mathnet  crossref  elib
    3. V. O. Mironkin, “Collisions and incidence of vertices and components in the graph of $k$-fold iteration of the uniform random mapping”, Discrete Math. Appl., 31:4 (2021), 259–269  mathnet  crossref  crossref  mathscinet  isi  elib
    4. V. O. Mironkin, “Raspredelenie dliny otrezka aperiodichnosti v grafe kompozitsii nezavisimykh ravnoveroyatnykh sluchainykh otobrazhenii”, Matem. vopr. kriptogr., 10:3 (2019), 89–99  mathnet  crossref
    5. V. O. Mironkin, “Sloi v grafe kompozitsii nezavisimykh ravnoveroyatnykh sluchainykh otobrazhenii”, Matem. vopr. kriptogr., 11:1 (2020), 101–114  mathnet  crossref
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