λ-fold indecomposable large sets of Steiner triple systems

Abstract

A family (X, B1),(X, B2) ,..., (X, Bq )o fq STS(v)s is a λ-fold large set of STS(v) and denoted by LSTSλ(v) if every 3-subset of X is contained in exactly λ STS(v)s of the collection. It is indecomposable and denoted by IDLSTSλ(v) if there exists no LSTSλ(v) contained in the collection for any λ� 1 and orders v ≡ 1, 3( mod 6) do there exist IDLSTS λ(v)? In this paper, we use partitionable candelabra systems (PCSs) and holey λ-fold large set of STS(v )( HLSTS λ(v)) as auxiliary designs to establish a recursive construction for IDLSTSλ(v) and show that there exists an IDLSTSλ(v) for λ =2 ,3, 4a ndv ≡ 1, 3( mod 6).