Abstract
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 that maps β to β−1, where β −1 = {(c,b,a)|(a,b,c) E β}. In this article we give necessary and sufficient conditions for the existence of a Directed triple system of order v admitting an antiautomorphism consisting of a single cycle of length d and having v − d fixed points. Further, we give a more general result for partial Directed triple systems in which the missing ordered pairs are precisely those containing two fixed points. © 1996 John Wiley & Sons, Inc.
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