On overlarge sets of Kirkman triple systems

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