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IMCS/Publications/BASM/Issues/BASM n.3 (49), 2005/

Pairwise orthogonality of n-ary operations.

Authors: Beliavscaia Galina

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.

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