Geodesic
Pairwise orthogonality of $n$-ary operations
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2005), pp. 5-18

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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. 
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     author = {G. Belyavskaya},
     title = {Pairwise orthogonality of $n$-ary operations},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {5--18},
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     number = {3},
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G. Belyavskaya. Pairwise orthogonality of $n$-ary operations. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2005), pp. 5-18. http://geodesic.mathdoc.fr/item/BASM_2005_3_a1/