Cyclically Indecomposable Triple Systems that are Decomposable

In this paper we investigate exhaustively the cyclically indecomposable triple systems T Sλ(v) for λ = 2, v ≤ 33 and λ = 3, v ≤ 21 and we identify the decomposable ones. We also construct, by using Skolem-type and Rosa-type sequences, cyclically indecomposable twofold triple systems T S2(v) for all admissible orders. Further, we investigate exhaustively all cyclic T S2(v) that are constructed by Skolemtype and Rosa-type sequences up to v ≤ 45 for indecomposability.