Minimal defining sets in a family of Steiner triple systems

Sets of three pairwise orthogonal Steiner triple systems

Two Steiner triple systems (STS) are orthogonal if their sets of triples are disjoint, and two disjoint pairs of points defining intersecting triples in one system fail to do so in the other. In 1994, it was shown [2] that there exist a pair of orthogonal Steiner triple systems of order v for all v ≡ 1, 3 (mod 6), with v ≥ 7, v 6= 9. In this paper we show that there exist three pairwise orthogo...

Steiner Trades That Give Rise to Completely Decomposable Latin Interchanges

In this paper we focus on the representation of Steiner trades of volume less than or equal to nine and identify those for which the associated partial latin square can be decomposed into six disjoint latin interchanges. 1 Background information In any combinatorial configuration it is possible to identify a subset which uniquely determines the structure of the configuration and in some cases i...

Doubling and Tripling Constructions for Defining Sets in Steiner Triple Systems

Isomorphisms of Infinite Steiner Triple Systems

An infinite countable Steiner triple system is called universal if any countable Steiner triple system can be embedded into it. The main result of this paper is the proof of non-existence of a universal Steiner triple system. The fact is proven by constructing a family S of size 2 of infinite countable Steiner triple systems so that no finite Steiner triple system can be embedded into any of th...

Large sets of large sets of Steiner triple systems of order 9

We describe a direct method of partitioning the 840 Steiner triple systems of order 9 into 120 large sets. The method produces partitions in which all of the large sets are isomorphic and we apply the method to each of the two non-isomorphic large sets of STS(9). AMS classification: 05B07.