More results on large sets of Kirkman triple systems

TL;DR

This paper introduces a new combinatorial structure called RDSQS* and uses it to construct larger resolvable designs, leading to new infinite families of large sets of Kirkman triple systems, advancing the understanding of this open problem.

Contribution

The paper presents a novel combinatorial structure RDSQS* and a recursive construction method for RDSQS(4v), resulting in new infinite families of LKTSs.

Findings

New infinite families of LKTSs are constructed.

Introduction of the RDSQS* structure for recursive design construction.

Enhanced methods for building large sets of Kirkman triple systems.

Abstract

The existence of large sets of Kirkman triple systems (LKTSs) is one of the best-known open problems in combinatorial design theory. Steiner quadruple systems with resolvable derived designs (RDSQSs) play an important role in the recursive constructions of LKTSs. In this paper, we introduce a special combinatorial structure RDSQS*(v) and use it to present a construction for RDSQS(4v). As a consequence, some new infinite families of LKTSs are given.