Mendelsohn directed triple systems

AbstractWe introduce a class of ordered triple systems which are both Mendelsohn triple systems and directed triple systems. We call these Mendelsohn directed triple systems (MDTS(v,λ)), characterise them, and prove that they exist if and only if λ(v−1)≡0(mod3). This is the same spectrum as that of regular directed triple systems, of which they are a special case. We also prove that cyclic MDTS(v,λ) exist if and only if λ(v−1)≡0(mod6) . In so doing we simplify a known proof of the existence of cyclic directed triple systems. Finally, we enumerate some ‘small’ MDTS