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We demonstrate a novel approach for the random sampling of Latin squares oforder~$n$ via probabilistic divide-and-conquer. The algorithm divides theentries of the table modulo powers of $2$, and samples a corresponding binarycontingency table at each level. The sampling distribution is based on theBoltzmann sampling heuristic, along with probabilistic divide-and-conquer.

Random sampling of Latin squares via binary contingency tables and probabilistic divide-and-conquer