Geodesic
On the use of binary operations for the construction of a multiply transitive class of block transformations
Diskretnaya Matematika, Tome 32 (2020) no. 2, pp. 85-111.

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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. 
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     title = {On the use of binary operations for the construction of a multiply transitive class of block transformations},
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     url = {http://geodesic.mathdoc.fr/item/DM_2020_32_2_a6/}
}
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I. V. Cherednik. On the use of binary operations for the construction of a multiply transitive class of block transformations. Diskretnaya Matematika, Tome 32 (2020) no. 2, pp. 85-111. http://geodesic.mathdoc.fr/item/DM_2020_32_2_a6/

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[2] Cherednik I. V., “Odin podkhod k postroeniyu tranzitivnogo mnozhestva blochnykh preobrazovanii”, Prikladnaya diskretnaya matematika, 38 (2017), 5–34

[3] Cherednik I. V., “Odin podkhod k postroeniyu kratno tranzitivnogo mnozhestva blochnykh preobrazovanii”, Prikladnaya diskretnaya matematika, 42 (2018), 18–47

[4] Cherednik I. V., “Ob ispolzovanii binarnykh operatsii pri postroenii tranzitivnogo mnozhestva blochnykh preobrazovanii”, Diskretnaya matematika, 31 (2019), 93–113