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Bul. Acad. Ştiinţe Repub. Mold. Mat., 2005, Number 3, Pages 5–18 (Mi basm133)  

This article is cited in 1 scientific paper (total in 1 paper)

Pairwise orthogonality of $n$-ary operations

G. Belyavskaya

Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, Chisinau, Moldova

Abstract: The notions of hypercube and of the orthogonality of two hypercubes were arised in combinatorial analysis. In [11] a connection between $n$-dimensional hypercubes and algebraic $n$-ary operations was established. In this article we use an algebraic approach to the study of orthogonality of two hypercubes (pairwise orthogonality). We give a criterion of orthogonality of two finite $k$-invertible $n$-ary operations, which is used by the research of orthogonality and parastrophe-orthogonality of two $n$-ary $T$-quasigroups. Some examples are given and connection between admissibility and pairwise orthogonality of $n$-ary operations is established.

Keywords and phrases: Hypercube, orthogonal hypercubes, $n$-ary operation, $n$-ary quasigroup, $n$-ary $T$-quasigroup, parastrophe, transversal, orthogonal $n$-ary \linebreak operations.

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Bibliographic databases:

MSC: 20N05, 20N15
Received: 09.11.2005
Language: English

Citation: G. Belyavskaya, “Pairwise orthogonality of $n$-ary operations”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2005, no. 3, 5–18

Citation in format AMSBIB
\Bibitem{Bel05}
\by G.~Belyavskaya
\paper Pairwise orthogonality of $n$-ary operations
\jour Bul. Acad. \c Stiin\c te Repub. Mold. Mat.
\yr 2005
\issue 3
\pages 5--18
\mathnet{http://mi.mathnet.ru/basm133}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2225091}
\zmath{https://zbmath.org/?q=an:1148.20310}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. G. Belyavskaya, “Power sets of $n$-ary quasigroups”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2007, no. 1, 37–45  mathnet  mathscinet  zmath
  • Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
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