Computing random rr-orthogonal Latin squares

Abstract

Two Latin squares of order nn are rr-orthogonal if, when superimposed, there are exactly rr distinct ordered pairs. The spectrum of all values of rr for Latin squares of order nn is known. A Latin square AA of order nn is rr-self-orthogonal if AA and its transpose are rr-orthogonal. The spectrum of all values of rr is known for all orders n14n\ne 14. We develop randomized algorithms for computing pairs of rr-orthogonal Latin squares of order nn and algorithms for computing rr-self-orthogonal Latin squares of order nn

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