Перегляд за Автор "Fryz, Iryna V."

Зараз показуємо 1 - 3 з 3
  • Ескіз недоступний
    Документ
    Algorithm for the complement of orthogonal operations
    (Prague, Czech Republic: COMMENTATIONES MATHEMATICAE UNIVERSITATIS CAROLINAE, 2018-02-15) Fryz, Iryna V.
    G. B. Belyavskaya and G. L. Mullen showed the existence of a comple ment for a k-tuple of orthogonal n-ary operations, where k < n, to an n-tuple of orthogonal n-ary operations. But they proposed no method for complementing. In this article, we give an algorithm for complementing a k-tuple of orthogonal n-ary operations to an n-tuple of orthogonal n-ary operations and an algorithm for complementing a k-tuple of orthogonal k-ary operations to an n-tuple of orthogonal n-ary operations. Also we find some estimations of the number of complements.
  • Ескіз недоступний
    Документ
    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.
  • Ескіз недоступний
    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/