In this paper, we give some decompositions of triples of Zp^n or Z3p^n into cyclic triple systems. New constructions of difference families are given. Some infinite classes of simple cyclic triple systems are obtained...In this paper, we give some decompositions of triples of Zp^n or Z3p^n into cyclic triple systems. New constructions of difference families are given. Some infinite classes of simple cyclic triple systems are obtained from these decompositions.展开更多
In this article, we establish the existence of an LHMTS（mv） for v ≡ 2 （mod 6） and m≡ 3 （mod 6）. Thus there exists an LHMTS（mv） if and only if v（v-1）m2 ≡ 0 （mod 3） except possibly for v=6, m≡ 1, 5 （mo...In this article, we establish the existence of an LHMTS（mv） for v ≡ 2 （mod 6） and m≡ 3 （mod 6）. Thus there exists an LHMTS（mv） if and only if v（v-1）m2 ≡ 0 （mod 3） except possibly for v=6, m≡ 1, 5 （mod 6） and m≠1. In the similar way, the existence of LHDTS（mv） is completely determined, i.e., there exists an LHDTS（mv） if and only if v（v-1）m2 ≡ 0 （mod 3）.展开更多
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 indecomposab...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）.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.11071056 and 10971051)supported by Natural Science and Engineering Research Council of Canada(Grant No.239135-06)
文摘In this paper, we give some decompositions of triples of Zp^n or Z3p^n into cyclic triple systems. New constructions of difference families are given. Some infinite classes of simple cyclic triple systems are obtained from these decompositions.
基金Supported by National Natural Science Foundation of China(Grant Nos.11471096 and 11771119)
文摘In this article, we establish the existence of an LHMTS（mv） for v ≡ 2 （mod 6） and m≡ 3 （mod 6）. Thus there exists an LHMTS（mv） if and only if v（v-1）m2 ≡ 0 （mod 3） except possibly for v=6, m≡ 1, 5 （mod 6） and m≠1. In the similar way, the existence of LHDTS（mv） is completely determined, i.e., there exists an LHDTS（mv） if and only if v（v-1）m2 ≡ 0 （mod 3）.
基金Supported by National Natural Science Foundation of China (Grant Nos. 10971051 and 11071056)
文摘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）.
