λ-fold indecomposable large sets of Steiner triple
systems
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【期刊名称】《中国科学》 【年(卷),期】2010(000)011
【摘要】A family (X, B1), (X, B2), . . . , (X, Bq) of q 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 < λ. In 1995, Griggs and Rosa posed a problem: For which values of λ > 1 and orders v ≡ 1, 3 (mod 6) do there exist IDLSTSλ(v)? In this paper, we use partitionable candelabra systems (PCSs) and holey λ-fold large set of STS(v) (HLSTSλ(v)) as auxiliary designs to establish a recursive construction for IDLSTSλ(v) and show that there exists an IDLSTSλ(v) for λ = 2, 3, 4 and v ≡ 1, 3 (mod 6). 【总页数】12页(P.2877-2888) 【
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Steiner;triple;system;large;set;candelabra;system;indecomposable 【作者】佚名 【作者单位】; 【正文语种】英文 【中图分类】N
λ-fold indecomposable large sets of Steiner triple systems
