Some bicyclic antiautomorphisms of directed triple systems

Bicyclic antiautomorphisms of directed triple systems with 0 or 1 fixed points

A transitive triple, (a, b, e), is defined to be the set {(a, b), (b, e), (a, en of ordered pairs. A directed triple system of order v, DTS(v), is a pair (D, (3), where D is a set of v points and (3 is a collection of transitive triples of pairwise distinct points of D such that any ordered pair of distinct points of D is contained in precisely one transitive triple of (3. An antiautomorphism o...

On the directed triple systems with a given automorphism

A directed triple system of order v, denoted DTS(v), is said to be f-bicyclic if it admits an automorphism consisting of f fixed points and two disjoint cycles. In this paper, we give necessary and sufficient conditions for the existence of f-bicyclic

A class of antiautomorphisms of Mendelsohn triple systems with two cycles

Bicyclic Mixed Triple Systems

Bicyclic Mixed Triple Systems by Benkam Benedict Bobga In the study of triple systems, one question faced is that of finding for what order a decomposition exists. We state and prove a necessary and sufficient condition for the existence of a bicyclic mixed triple system based on the three possible partial orientations of the 3-cycle with twice as many arcs as edges. We also explore the existen...

Mendelsohn directed triple systems

We 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 (mod 3). 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,...