Directed Triple Systems with a Class of Automorphisms

Abstract

A directed triple system of order $v$, denoted by $DTS(v)$, is called $(f,k)$-rotational if it has an automorphism consisting of $f$ fixed points and $k$ cycles each of length $(v-f)/k$. In this paper, we obtain a necessary and sufficient condition for the existence of $(f,k)$-rotational $DTS(v)$ for any arbitrary positive integer $k$.