The spectrum of bicyclic antiautomorphisms of directed triple systems Original Research Article

A transitive triple, (a,b,c), is defined to be the set {(a,b),(b,c),(a,c)} of ordered pairs. A directed triple system of order v, DTS(v), is a pair (D,β), where D is a set of v points and β 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 β. An antiautomorphism of a directed triple system, (D,β), is a permutation of D which maps β to β−1, where β−1={(c,b,a)|(a,b,c)∈β}. In this paper we complete the necessary and sufficient conditions for the existence of a directed triple system of order v admitting an antiautomorphism consisting of two cycles.