On the existence of partitionable skew Room frames

Partitionable skew Room frames of type hⁿ have played an important role in the constructions of 4-frames, (K₄-e)-frames and super-simple (4,2)-frames. In this paper, we investigate the existence of partitionable skew Room frames of type hⁿ. The necessary conditions for the existence of such a design are that and h?5. It is proved that these necessary conditions are also sufficient with a few possible exceptions. As a byproduct, the known results on the existence of skew Room frames and uniform 4-frames are both improved.