On Kirkman triple systems of order 33

Kirkman Triple Systems of Orders 27 , 33 , and 39

In the search for doubly resolvable Kirkman triple systems of order v, systems admitting an automorphism of order (v 3)=3 fixing three elements, and acting on the remaining elements in three orbits of length (v 3)=3, have been of particular interest. We have established by computer that 100 such Kirkman triple systems exist for v = 21, 81,558 for v = 27, at least 4,494,390 for v = 33, and at le...

Kirkman triple systems of order 21 with nontrivial automorphism group

There are 50,024 Kirkman triple systems of order 21 admitting an automorphism of order 2. There are 13,280 Kirkman triple systems of order 21 admitting an automorphism of order 3. Together with the 192 known systems and some simple exchange operations, this leads to a collection of 63,745 nonisomorphic Kirkman triple systems of order 21. This includes all KTS(21)s having a nontrivial automorphi...

Intersection Numbers of Kirkman Triple Systems

A Steiner triple system of order v (briefly STS(v)) is a pair (X, B) where X is a v-set and B is a collection of 3-subset of X (called triple) such that every pair of distinct elements of X belongs to exactly one triple of B. A Kirkman triple system of order v (briefly KTS(v)) is a Steiner triple system of order v (X, B) together with a partition R of the set of triples B into subsets R1 , R2 ,...

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.

A Completion Conjecture for Kirkman Triple Systems