Construction of large sets of pairwise disjoint transitive triple systems II

A construction for large sets of disjoint Kirkman triple systems

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...

A Completion of the Spectrum for Large Sets of Disjoint Transitive Triple Systems

In what follows, an ordered pair will always be an ordered pair (x, y), where x # y. A transitive triple is a collection of three ordered pairs of the form (6, Y), (Y, z), (x, z)}, which we will always denote by (x, y, z). A transitive triple system (TTS(u)) is a pair (X, B), where X is a set containing v elements and B is a collection of transitive triples of elements of X such that every orde...

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...

A Construction of Disjoint Steiner Triple Systems

We show that there are at least 4t + 2 mutually disjoint, isomorphic Steiner triple systems on 6t + 3 points, if t ;?: 4. MiS Subject Classification: OSBOS