Chow–Taylor conjecture on Latin wide Young diagrams

A Young diagram $Y$ is wide if, for every subset $S$ of its rows, the diagram formed by $S$ dominates its conjugate; a filling of $Y$ is Latin if it assigns to each row the numbers $1,\ldots,a_i$ injectively and is also injective in every column. Chow–Taylor's conjecture. If a Young diagram $Y$ is wide, then it is Latin. This is the converse of the theorem that every Latin Young diagram is wide; the paper states that it proves a weaker dual version, so the converse remains the conjectural claim considered here.