Transitive resolvable idempotent symmetric quasigroups and large sets of Kirkman triple systems

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 construction for large sets of disjoint Kirkman triple systems

Recursive constructions for large sets of resolvable hybrid triple systems

An improved product construction for large sets of Kirkman triple systems

It has been shown by Lei, in his recent paper, that there exists a large set of Kirkman triple systems of order uv (LKTS(uv)) if there exist an LKTS(v), a TKTS(v) and an LR(u), where a TKTS(v) is a transitive Kirkman triple system of order v, and an LR(u) is a new kind of design introduced by Lei. In this paper, we improve this product construction by removing the condition “there exists a TKTS...

Another Product Construction for Large Sets of Resolvable Directed Triple Systems

A large set of resolvable directed triple systems of order v, denoted by LRDTS(v), is a collection of 3(v − 2) RDTS(v)s based on v-set X, such that every transitive triple of X occurs as a block in exactly one of the 3(v − 2) RDTS(v)s. In this paper, we use DTRIQ and LR-design to present a new product construction for LRDTS(v)s. This provides some new infinite families of LRDTS(v)s.