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Diskr. Mat., 2020, Volume 32, Issue 2, Pages 85–111 (Mi dm1597)  

This article is cited in 2 scientific papers (total in 2 papers)

On the use of binary operations for the construction of a multiply transitive class of block transformations

I. V. Cherednik

Russian Technological University (MIREA)

Abstract: We continue to study the set of block transformations $\{\Sigma^F : F\in\mathcal B^*(\Omega)\}$ implemented by a binary network $\Sigma$ endowed with a binary operation $F$ invertible in the second variable. For an arbitrary $k\geqslant2$ we obtain necessary and sufficient conditions for $k$-transitivity of the set of transformations $\{\Sigma^F \colon F\in\mathcal B^*(\Omega)\}$, and propose an efficient method for checking whether these conditions hold. We also introduce two methods for construction of networks $\Sigma$ such that the sets of transformations $\{\Sigma^F\colon F\in\mathcal B^*(\Omega)\}$ are $k$-transitive.

Keywords: network, block transformation, $k$-transitive class of transformations

DOI: https://doi.org/10.4213/dm1597

Full text: PDF file (519 kB)
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English version:
Discrete Mathematics and Applications, 2021, 31:2, 91–111

Bibliographic databases:

UDC: 519.719.2
Received: 11.11.2019

Citation: I. V. Cherednik, “On the use of binary operations for the construction of a multiply transitive class of block transformations”, Diskr. Mat., 32:2 (2020), 85–111; Discrete Math. Appl., 31:2 (2021), 91–111

Citation in format AMSBIB
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\pages 85--111
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\jour Discrete Math. Appl.
\yr 2021
\vol 31
\issue 2
\pages 91--111
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  • https://doi.org/10.4213/dm1597
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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. I. V. Cherednik, “Ob odnom podkhode k postroeniyu kratno tranzitivnogo mnozhestva blochnykh preobrazovanii”, PDM. Prilozhenie, 2020, no. 13, 69–71  mathnet  crossref
    2. I. V. Cherednik, “Razvitie odnogo podkhoda k postroeniyu mnozhestva blochnykh biektivnykh preobrazovanii”, Matem. vopr. kriptogr., 12:3 (2021), 49–66  mathnet  crossref
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