4 problems

Drisko's conjecture. Either $A$ has a transversal, or $A$ can be transformed into $R_{2n-2,n}$ by permuting rows, columns, and symbols.

Disjoint-transversal conjecture. If $m\ge2n-1$, then $A$ has $m-(n-1)$ pairwise disjoint transversals.

For $k\leq n$, let $\mathcal{LR}_{k,n}$ be the set of $k\times n$ Latin rectangles with symbol set $[n]$. A partial Latin rectangle is $\beta n$-sparse if each row and column conta…

For $k\leq n$, let $\mathcal{LR}_{k,n}$ be the set of $k\times n$ Latin rectangles with symbol set $[n]$, and let $\randLR$ be chosen uniformly from this set. For every…