A Solution for the Embedding Problem for Partial Transitive Triple Systems

In this paper we solve the embedding problem for partial transitivetriple systems of order n and index , partial TTS(n, ) s, showingthat any partial TTS(n, ) can be embedded in a TTS(v, ) forall -admissible v 2n + 1. This lower bound on v is the bestpossible. A simple proof is also given of a result of Colbournand Harms which shows that every partial triple system of ordern and index 2 is the underlying triple system of a partial TTS(n,). 1991 Mathematics Subject Classification 05B07.