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This article is cited in 4 scientific papers (total in 4 papers)
Using binary operations to constructa transitive set of block transformations
I. V. Cherednik MIREA — Russian Technological University, Moscow
Abstract:
We study the set of transformations $\{\Sigma^F\colon F\in\mathcal B^*(\Omega)\}$ implemented by a network $\Sigma$ with a single binary operation $F$, where $\mathcal B^*(\Omega)$ is the set of all binary operations on $\Omega$ that are invertible as function of the second variable. We state a criterion of bijectivity of all transformations from the family $\{\Sigma^F\colon F\in\mathcal B^*(\Omega)\}$ in terms of the structure of the network $\Sigma$, identify necessary and sufficient conditions of transitivity of the set of transformations $\{\Sigma^F\colon F\in\mathcal B^*(\Omega)\}$, and propose an efficient way of verifying these conditions. We also describe an algorithm for construction of networks $\Sigma$ with transitive sets of transformations $\{\Sigma^F\colon F\in\mathcal B^*(\Omega)\}$.
Keywords:
network, block transformation, transitive class of block transformations.
Received: 24.12.2018 Revised: 15.08.2019
Citation:
I. V. Cherednik, “Using binary operations to constructa transitive set of block transformations”, Diskr. Mat., 31:3 (2019), 93–113; Discrete Math. Appl., 30:6 (2020), 375–389
Linking options:
https://www.mathnet.ru/eng/dm1580https://doi.org/10.4213/dm1580 https://www.mathnet.ru/eng/dm/v31/i3/p93
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Abstract page: | 307 | Full-text PDF : | 32 | References: | 28 | First page: | 11 |
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