On overlarge sets of Kirkman triple systems

The determination of the existence of large sets of Kirkman triple systems (LKTSLKTS) is a classical combinatorial problem. In this paper we introduce a new concept OLGKSOLGKS—overlarge sets of generalized Kirkman triple systems and show the relationship between the new concept and overlarge sets of Kirkman triple systems (OLKTS(v)OLKTS(v)). Further, some recursive constructions for OLGKSOLGKS are given, and some new existence results of OLKTS(v)OLKTS(v) with a special properties are obtained, which plays an important role in the discussion of large sets of Kirkman triple systems.