Indecomposable Large Sets of Steiner Triple Systems with Indices 5, 6  

作　　者：Mei Hui CHENG Zi Hong TIAN 

机构地区：[1]Institute of Mathematics,Hebei Normal University

出　　处：《Acta Mathematica Sinica,English Series》2012年第11期2169-2184,共16页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China (Grant Nos. 10971051 and 11071056)

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 A STS（v）s of the collection. It is indecomposable and denoted by IDLSTSx（v） if there does not exist an LSTSx, （v） contained in the collection for any λ 〈 λ. In this paper, we show that for λ = 5, 6, there is an IDLSTSλ（v） for v ≡ 1 or 3 （rood 6） with the exception IDLSTS6（7）.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 A STS（v）s of the collection. It is indecomposable and denoted by IDLSTSx（v） if there does not exist an LSTSx, （v） contained in the collection for any λ 〈 λ. In this paper, we show that for λ = 5, 6, there is an IDLSTSλ（v） for v ≡ 1 or 3 （rood 6） with the exception IDLSTS6（7）.

关 键 词：Steiner triple system  large set  candelabra system INDECOMPOSABLE 

分 类 号：O156[理学—数学]