Bul. Acad. Ştiinţe Repub. Mold. Mat., 2005, Number 3, Pages 5–18
This article is cited in 1 scientific paper (total in 1 paper)
Pairwise orthogonality of $n$-ary operations
Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, Chisinau, Moldova
The notions of hypercube and of the orthogonality of two hypercubes were arised in combinatorial analysis. In  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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MSC: 20N05, 20N15
G. Belyavskaya, “Pairwise orthogonality of $n$-ary operations”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2005, no. 3, 5–18
Citation in format AMSBIB
\paper Pairwise orthogonality of $n$-ary operations
\jour Bul. Acad. \c Stiin\c te Repub. Mold. Mat.
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This publication is cited in the following articles:
G. Belyavskaya, “Power sets of $n$-ary quasigroups”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2007, no. 1, 37–45
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