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arXiv · 2311.00992

Computing random $r$-orthogonal Latin squares

Sergey Bereg
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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 $n\ne 14$. 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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Sergey Bereg. 2023-11-02. Computing random $r$-orthogonal Latin squares. https://arxiv.org/abs/2311.00992

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