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Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.

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The condition for mutually orthogonal Latin square

Suppose $A$ and $B$ are Latin squares of order $n$. And suppose any column of $A$ and any column of $B$ have common entry only once. Then are $A$ and $B$ mutually orthogonal? I know the converse is tr …