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Diskr. Mat., 2019, Volume 31, Issue 4, Pages 38–52 (Mi dm1596)  

This article is cited in 1 scientific paper (total in 1 paper)

Collisions and incidence of vertices and components in the graph of $k$-fold iteration of the uniform random mapping

V. O. Mironkin

National Research University "Higher School of Economics", Moscow

Abstract: The probabilistic characteristics of the graph of $k$-fold iteration of uniform random mapping are studied. Formulas for the distribution of the length of the aperiodicity segment of an arbitrary vertex with some restrictions are calculated. We obtain exact expressions for the probabilities that two arbitrary vertices belong to the same connected component, that an arbitrary vertex belongs to the preimage set of another vertex and that there exists a collision in the considered graph.} \keywords{ uniform random mapping, iteration of random mapping, aperiodicity segment, graph of a mapping, connected component, preimage, collision

Keywords: uniform random mapping, iteration of random mapping, aperiodicity segment, graph of a mapping, connected component, preimage, collision

DOI: https://doi.org/10.4213/dm1596

Full text: PDF file (480 kB)
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English version:
Discrete Mathematics and Applications, 2021, 31:4, 259–269

Bibliographic databases:

UDC: 519.212.2+519.719.2
Received: 12.07.2019
Revised: 24.11.2019

Citation: V. O. Mironkin, “Collisions and incidence of vertices and components in the graph of $k$-fold iteration of the uniform random mapping”, Diskr. Mat., 31:4 (2019), 38–52; Discrete Math. Appl., 31:4 (2021), 259–269

Citation in format AMSBIB
\Bibitem{Mir19}
\by V.~O.~Mironkin
\paper Collisions and incidence of vertices and components in the graph of $k$-fold iteration of the uniform random mapping
\jour Diskr. Mat.
\yr 2019
\vol 31
\issue 4
\pages 38--52
\mathnet{http://mi.mathnet.ru/dm1596}
\crossref{https://doi.org/10.4213/dm1596}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=4043282}
\elib{https://elibrary.ru/item.asp?id=47042170}
\transl
\jour Discrete Math. Appl.
\yr 2021
\vol 31
\issue 4
\pages 259--269
\crossref{https://doi.org/10.1515/dma-2021-0023}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000691761800004}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85114302515}


Linking options:
  • http://mi.mathnet.ru/eng/dm1596
  • https://doi.org/10.4213/dm1596
  • http://mi.mathnet.ru/eng/dm/v31/i4/p38

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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, “Sloi v grafe kompozitsii nezavisimykh ravnoveroyatnykh sluchainykh otobrazhenii”, Matem. vopr. kriptogr., 11:1 (2020), 101–114  mathnet  crossref
  • Дискретная математика
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