Cyclically Indecomposable Triple Systems that are Decomposable

Abstract

In this paper, we investigate exhaustively the cyclically indecomposable triple systems $T{S}_{\lambda }(v)$ for $\lambda =2,v\le 33$ and $\lambda =3,v\le 21$, and we identify the decomposable ones. We also construct, by using Skolem-type and Rosa-type sequences, cyclically indecomposable two-fold triple systems $T{S}_2(v)$ for all admissible orders. Further, we investigate exhaustively all cyclic $T{S}_2(v)$ that are constructed by Skolem-type and Rosa-type sequences up to $v\le 45$ for indecomposability.