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Power sets of n-ary quasigroups.
Authors: Beliavscaia Galina
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Abstract
In the theory of latin squares and in the binary quasigroup theory the notion of a latin power set (a quasigroup power set) is known. These sets have a good property, and namely, they are orthogonal sets. Such sets were studied and methods of their construction were suggested in different articles (see, for example, [1-5]). In this article we introduce (k)-powers of a k-invertible n-ary operation (with respect to the k-multiplication of n-ary operations) and (k)-power sets of n-ary quasigroups, n≥2, 1≤k≤n, prove pairwise orthogonality of such sets and consider distinct posibilities of their construction with the help of binary groups, in particular, using n-T-quasigroups and n-ary groups.E-mail:
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Contents
- Pareto approximation of the tail by local exponential modeling.
- Classification of GL(2, ℜ)-orbit's dimensions for the differential equations' system with homogeneities of the 4th order.
- Power sets of n-ary quasigroups.
- Existence and uniqueness results for a class of nonlinear differential problems.
- Biharmonic curves in Cartan-Vranceanu (2n+1)-dimensional spaces.
- Infinitely many functional pre-complete classes of formulas in the propositional provability intuitionistic logic.
- Linear convolution of criteria in the vector p-center problem.
- On LCA groups in which some closed subgroups have commutative rings of continuous endomorphisms.
- Multi-dimensional Darboux type differential systems with quadratic nonlinearities.
- GL(2, ℜ) -orbits in a competing species model.
- Minimum Cost Multicommodity Flows in Dynamic Networks and Algorithms for their Finding.
