Self-converse Large Sets of Pure Mendelsohn Triple Systems  

作　　者：Jian Guo LEI Cui Ling FAN Jun Ling ZHOU 

机构地区：[1]Institute of Mathematics, Beijing Jiaotong University, Beijing 100044, P. R. China [2]Institute of Mathematics, Hebei Normal University, Shijiazhuang 050016, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2009年第10期1665-1680,共16页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China (Grant No.10771051)

摘　　要：A Mendelsohn triple system of order v （MTS（v）） is a pair （X,B） where X is a v-set and 5g is a collection of cyclic triples on X such that every ordered pair of X belongs to exactly one triple of B. An MTS（v） （X,B） is called pure and denoted by PMTS（v） if （x, y, z） ∈ B implies （z, y, x） ∈B. A large set of MTS（v）s （LMTS（v）） is a collection of v - 2 pairwise disjoint MTS（v）s on a v-set. A self-converse large set of PMTS（v）s, denoted by LPMTS＊ （v）, is an LMTS（v） containing [ v-2/2] converse pairs of PMTS（v）s. In this paper, some results about the existence and non-existence for LPMTS＊ （v） are obtained.A Mendelsohn triple system of order v （MTS（v）） is a pair （X,B） where X is a v-set and 5g is a collection of cyclic triples on X such that every ordered pair of X belongs to exactly one triple of B. An MTS（v） （X,B） is called pure and denoted by PMTS（v） if （x, y, z） ∈ B implies （z, y, x） ∈B. A large set of MTS（v）s （LMTS（v）） is a collection of v - 2 pairwise disjoint MTS（v）s on a v-set. A self-converse large set of PMTS（v）s, denoted by LPMTS＊ （v）, is an LMTS（v） containing [ v-2/2] converse pairs of PMTS（v）s. In this paper, some results about the existence and non-existence for LPMTS＊ （v） are obtained.

关 键 词：large set Mendelsohn triple system CONVERSE good large set partitionable Mendelsohn Candelabra system 

分 类 号：O157[理学—数学] O157.2[理学—基础数学]