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Let $\Pi=\{\pi_1,\pi_2,\dots,\pi_n\}$ be the rows of an $n\times n$ Latin square (the order of the rows does not matter). Each row $\pi_i$ induces an order $\prec_i$ on the elements of $[1,n]$, where $...

Cross posting from MSE, where this question received no answers. The following Latin square $$\begin{bmatrix} 1&2&3&4&5&6&7&8\\ 2&1&4&5&6&7&8&3\\...

Let $M \in \mathbb{N}$ and let $\pi \in S_{M}$ be an involution with at least one fixed point. I'm interested in finding a latin square $A$ of order $M$ such that $A_{i,j} = \pi(A_{j,i})$ for each $i,...

Sixy Sudoku is a variation on Latin squares and traditional sudoku played on a $6 \times 6$ grid with an initial clue of several cells filled in with a subset of the digits $1$–$6$. The task is to ...