On the existence of partitionable skew Room frames

Partitionable skew Room frames of type hnhn have played an important role in the constructions of 4-frames, (K4-e)(K4-e)-frames and super-simple (4,2)(4,2)-frames. In this paper, we investigate the existence of partitionable skew Room frames of type hnhn. The necessary conditions for the existence of such a design are that h(n-1)≡0(mod4) and h⩾5h⩾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.