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The construction of orthogonal k-skeins and latin k-cubes. (English) Zbl 0334.05023

MSC:
05B15 Orthogonal arrays, Latin squares, Room squares
20N15 \(n\)-ary systems \((n\ge 3)\)
20N05 Loops, quasigroups
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References:
[1] Arkin, J.,A solution to the classical problem of finding systems of three mutually orthogonal numbers in a cube formed by three superimposed 10 \(\times\) 10 \(\times\) 10cubes. Fibonacci Quart.11 (1973), 485–489. Also Sugaku Seminar13 (1974), 90–94. · Zbl 0362.05039
[2] Arkin, J. andStraus, E. G.,Latin k-cubes. Fibonacci Quart.12 (1974), 288–292. · Zbl 0272.05017
[3] Bose, R. C., Shrikhande, S. S., andParker, E. T.,Further results on the construction of mutually orthogonal Latin squares and the falsity of Euler’s conjecture. Canad. J. Math.12 (1960), 189–203. · Zbl 0093.31905 · doi:10.4153/CJM-1960-016-5
[4] Evans, T.,Homomorphisms of non-associative systems. J. London Math. Soc.24 (1949), 254–260. · Zbl 0034.01304 · doi:10.1112/jlms/s1-24.4.254
[5] Evans, T.,Algebraic structures associated with orthogonal arrays and Latin squares. A summary of this paper will appear in the Proceedings of the Seminar on Algebraic Aspects of Combinatorics, University of Toronto, January 1975; to be published by Utilitas Mathematica.
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