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Orthogonality Generalized

The concept of orthogonality of Latin squares
can, of course, be generalized.

The following is from A.E. Brouwer, Chapter 5,
"Recursive Constructions of Mutually Orthogonal Latin Squares,"
pp. 149-168 of Latin Squares:
New Developments in the Theory and Applications
J. Denes and A. D. Keedwell, editors,
Annals of Discrete Mathematics, 46, North-Holland, 1991.

For an earlier (1978) instance
of this generalized
concept of orthogonality, see

Orthogonality of Latin Squares
Viewed as Skewness of Lines

and Latin-Square Geometry.

-- Steven H. Cullinane