P/N positions for Queen on general partitions

Characterize the winning and losing positions for the Queen game on general integer partitions.

Background

The Queen game allows horizontal, vertical, and diagonal moves on Young diagrams. The paper relates Queen on rectangular partitions to Wythoff’s game and proves several sufficient conditions for winning positions on arbitrary partitions, but it does not provide a complete characterization outside the rectangular setting.

The unresolved problem is to determine the P/N-position structure for Queen on general partitions. The authors note that even the rectangular case has a complicated resolution, making the extension to more general partitions difficult.