Using binary operations to construct a transitive set of block transformations
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Igor V. Cherednik
Abstract
We study the set of transformations {ΣF : F∈ 𝓑∗(Ω)} implemented by a network Σ with a single binary operation F, where 𝓑∗(Ω) is the set of all binary operations on Ω that are invertible as function of the second variable. We state a criterion of bijectivity of all transformations from the family {ΣF : F∈ 𝓑∗(Ω)} in terms of the structure of the network Σ, identify necessary and sufficient conditions of transitivity of the set of transformations {ΣF : F∈ 𝓑∗(Ω)}, and propose an efficient way of verifying these conditions. We also describe an algorithm for construction of networks Σ with transitive sets of transformations {ΣF : F∈ 𝓑∗(Ω)}.
Originally published in Diskretnaya Matematika (2019) 31,№3, 93–113 (in Russian).
References
[1] Belousov V.D., Fundamentals of quasigroups and loops theory M.: Nauka, 1967 (in Russian).Suche in Google Scholar
[2] Cherednik I. V., “One approach to transitive set construction of block transformations”, Prikladnaya Diskretnaya Matematika 38 (2017), 5–34 (in Russian).10.17223/20710410/38/1Suche in Google Scholar
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Artikel in diesem Heft
- Frontmatter
- Group polynomials over rings
- Maximum subclasses in classes of linear automata over finite fields
- Using binary operations to construct a transitive set of block transformations
- Perfect matchings and K1,p-restricted graphs
- On the waiting times to repeated hits of cells by particles for the polynomial allocation scheme
- Semibinomial conditionally nonlinear autoregressive models of discrete random sequences: probabilistic properties and statistical parameter estimation
Artikel in diesem Heft
- Frontmatter
- Group polynomials over rings
- Maximum subclasses in classes of linear automata over finite fields
- Using binary operations to construct a transitive set of block transformations
- Perfect matchings and K1,p-restricted graphs
- On the waiting times to repeated hits of cells by particles for the polynomial allocation scheme
- Semibinomial conditionally nonlinear autoregressive models of discrete random sequences: probabilistic properties and statistical parameter estimation
