Large sets of oriented triple systems with resolvability

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.

On Large Sets of Disjoint Steiner Triple Systems II

A Steiner system S(t, k, V) is a pair (S, /3), where S is a v-set and p is a collection of k-subsets of S called hocks, such that a t-subset of S occurs in exactly one block of p. In particular, an S(2, 3, V) is called a Steiner triple system of order v (briefly STS(v)). It is well known that there is an STS(v) if and only if v E 1 or 3 (mod 6). Two STSs, (S, /3,) and (S, &), are said to be dis...

Further results about large sets of disjoint Mendelsohn triple systems

Kang, Q. and Y. Chang, Further results about large sets of disjoint Mendelsohn triple systems, Discrete Mathematics 118 (I 993) 2633268. In this note, a construction of the large sets of pairwise disjoint Mendelsohn triple systems of order 72k + 6, where k > 1 and k F 1 or 2 (mod 3), is given. Let X be a set of v elements (v 2 3). A cyclic triple from X is a collection of three pairs (x, y), (y...

Further results on large sets of Kirkman triple systems

LR design is introduced by the second author in his recent paper, and it plays a very important role in the construction of LKTS (a large set of disjoint Kirkman triple system). In this paper, we generalize it and introduce a new design RPICS. Some constructions for these two designs are also presented. With the relationship between them and LKTS, we obtain some new LKTSs.

Recursive constructions for large sets of resolvable hybrid triple systems