Particular \(1,M,N\)-antiautomorphisms of directed triple systems (Q2799851)

A directed triple system is a pair \((D,\mathcal{T})\) where \(\mathcal{T}\) is a collection of transitive triples \((a,b,c)=\{(a,b),(a,c),(b,c)\}\) of elements of a set \(D\) such that each ordered pair of elements of \(D\) occurs in exactly one transitive triple of \(\mathcal{T}\).NEWLINENEWLINEIn this paper, a sufficient condition for the existence of an anti-automorphism (a permutation on \(D\) that maps \(\mathcal{T}\) to \(\mathcal{ T}^{-1}=\{(c,b,a);(a,b,c)\in \mathcal{T}\}\) with given properties is provided.