Computing random r-orthogonal Latin squares

2023/11/02 by Bereg, Sergey
#Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics

paper · doi:10.48550/arxiv.2311.00992

Abstract

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

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