λ-fold indecomposable large sets of Steiner triple systems  

作　　者：JI LiJun1, TIAN ZiHong2, & KANG QingDe2 1Department of Mathematics, Suzhou University, Suzhou 215006, China 2College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang 050016, China 

出　　处：《Science China Mathematics》2010年第11期2877-2888,共12页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant Nos.10971051, 10701060, 10831002);Qing Lan Project of Jiangsu Province, China

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).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).

关 键 词：STEINER TRIPLE SYSTEM large SET candelabra SYSTEM INDECOMPOSABLE 

分 类 号：O144[理学—数学]