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

  • Igor V. Cherednik EMAIL logo
Published/Copyright: April 7, 2021
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Discrete Mathematics and Applications
From the journal Discrete Mathematics and Applications Volume 31 Issue 2

Abstract

We continue to study the set of block transformations {ΣF:F∈B∗(Ω)} implemented by a binary network Σ endowed with a binary operation F invertible in the second variable. For an arbitrary k⩾2 we obtain necessary and sufficient conditions for k-transitivity of the set of transformations {ΣF:F∈B∗(Ω)}, and propose an efficient method for checking whether these conditions hold. We also introduce two methods for construction of networks Σ such that the sets of transformations {ΣF:F∈B∗(Ω)} are k-transitive.

Keywords: network; block transformation; k-transitive class of transformations

Note

Originally published in Diskretnaya Matematika (2020) 32,№2, 85–111 (in Russian).

References

[1] Belousov V. D., Foundations of quasigroups and loops theory, Nauka, Moscow, 1967.Search in Google Scholar

[2] Cherednik I. V., “One approach to transitive set construction of block transformations”, PrikladnayaDiskretnayaMatematika, 38 (2017), 5–34 (in Russian).10.17223/20710410/38/1Search in Google Scholar

[3] Cherednik I. V., “One approach to multiply transitive set construction of block transformations”, Prikladnaya Diskretnaya Matematika, 42 (2018), 18–47 (in Russian).10.17223/20710410/42/2Search in Google Scholar

[4] Cherednik I. V., “Using binary operations to construct a transitive set of block transformations”, Discrete Math. Appl., 30 (2020), 375–389.10.1515/dma-2020-0035Search in Google Scholar

Received: 2019-11-11
Accepted: 2019-08-15
Published Online: 2021-04-07
Published in Print: 2021-04-27

© 2021 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. Two-sided problem for the random walk with bounded maximal increment
  3. On the use of binary operations for the construction of a multiply transitive class of block transformations
  4. On the complexity of implementation of a system of two monomials by composition circuits
  5. On the degree of restrictions of q-valued logic vector functions to linear manifolds
  6. Trees with a given number of leaves and the maximal number of maximum independent sets
  7. Size distribution of the largest component of a random A-mapping
https://doi.org/10.1515/dma-2021-0009
Keywords for this article
network; block transformation; k-transitive class of transformations

Articles in the same Issue

  1. Frontmatter
  2. Two-sided problem for the random walk with bounded maximal increment
  3. On the use of binary operations for the construction of a multiply transitive class of block transformations
  4. On the complexity of implementation of a system of two monomials by composition circuits
  5. On the degree of restrictions of q-valued logic vector functions to linear manifolds
  6. Trees with a given number of leaves and the maximal number of maximum independent sets
  7. Size distribution of the largest component of a random A-mapping
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