Martin Grüttmüller, Nabil Shalaby, Rolf Rees
Cyclically Indecomposable Triple Systems that are Decomposable
Preprint series: Preprints aus dem Fachbereich Mathematik, Universität Rostock
MSC:
05B07 Triple systems
Abstract: In this paper we investigate exhaustively the cyclically indecomposable triple systems $TS_\lambda (v)$ for $\lambda=2$, $v \leq 33$ and $\lambda=3, v\leq 21$ and we identify the decomposable ones. We also construct, by using Skolem-type and Rosa-type sequences, cyclically indecomposable two-fold triple systems $TS_2(v)$ for all admissible orders. Further, we investigate exhaustively all cyclic $TS_2(v)$ that are constructed by Skolem-type and Rosa-type sequences up to $v \leq 45$ for indecomposability.
Keywords: triple system, Skolem sequence, Rosa sequence, indecomposable, decomposable