Перегляд за Автор "Sokhatsky, Fedir M."

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    Block composition algorithm for constructing orthogonal n-ary operations
    (journal homepage: www.elsevier.com/locate/disc, 2017-08-09) Fryz, Iryna V.; Sokhatsky, Fedir M.
    We propose an algorithm for constructing orthogonal n-ary operations which is called a block composition algorithm here. Input data of the algorithm are two series of differ ent arity operations being distributed by blocks. The algorithm consists of two parts: composition algorithm for constructing n-ary operations with orthogonal retracts from given blocks of operations and block-wise recursive algorithm for constructing orthogonal n-ary operations from obtained operations. Obtained results are illustrated by examples of orthogonal n-ary operations which are constructible by block-wise recursive algorithm and non-constructible by the well-known trivial recursive algorithm.
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    Документ
    Invertibility criterion of composition of two multiary quasigroups
    (Czech Republic: COMMENTATIONES MATHEMATICAE UNIVERSITATIS CAROLINAE, 2012) Sokhatsky, Fedir M.; Fryz, Iryna V.
    We study the Invertibility of operations that are a composition of two operations of arbitrary arities. We find the criterion for quasigroups and specifications for T-quasigroups. For this purpose, we introduce notions of perpendicularity of operations and hypercubes. They differ from the previously introduced notions of orthogonality of operations and hypercubes [G. Belyavskaya, G. Mullen, Orthogonal hypercubes and n-ary operations, Quasigroups Related System 13 (2005), no. 1, 73-86]/ we establish some relations between these notions and give illustrative examples/