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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{DM_2020_32_2_a6,
     author = {I. V. Cherednik},
     title = {On the use of binary operations for the construction of a multiply transitive class of block transformations},
     journal = {Diskretnaya Matematika},
     pages = {85--111},
     publisher = {mathdoc},
     volume = {32},
     number = {2},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2020_32_2_a6/}
}
TY  - JOUR
AU  - I. V. Cherednik
TI  - On the use of binary operations for the construction of a multiply transitive class of block transformations
JO  - Diskretnaya Matematika
PY  - 2020
SP  - 85
EP  - 111
VL  - 32
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DM_2020_32_2_a6/
LA  - ru
ID  - DM_2020_32_2_a6
ER  - 
%0 Journal Article
%A I. V. Cherednik
%T On the use of binary operations for the construction of a multiply transitive class of block transformations
%J Diskretnaya Matematika
%D 2020
%P 85-111
%V 32
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DM_2020_32_2_a6/
%G ru
%F DM_2020_32_2_a6
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/