Frame Self-orthogonal Mendelsohn Triple Systems

作     者：YunQingXU HanTaoZHANG 

作者机构：DepartmentofMathematicsNorthernJiaotongUniversityBeijing100044P.R.China ComputerScienceDepartmentTheUniversityofIowaIowaCityIA52242USA 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2004年第20卷第5期

页      面：913-924页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Research supported by NSFC 10371002 Partially supported by National Science Foundation under Grant CCR-0098093 

主　　题：Mendelsohn triple system Latin square Quasigroup Group divisible design 

摘      要：A Mendelsohn triple system of order v,MTS(v)for short,is a pair(X,B)where X is a v-set(of points)and B is a collection of cyclic triples on X such that every ordered pair of distinct points from X appears in exactly one cyclic triple of *** cyclic triple(a,b,c)contains the ordered pairs(a,b),(b,c)and(c,a).An MTS(v)corresponds to an idempotent semisymmetric Latin square (quasigroup)of order *** MTS(v)is called frame self-orthogonal,FSOMTS for short,if its associated semisymmetric Latin square is frame *** is known that an FSOMTS(1~n)exists for all n≡1(mod 3)except n=10 and for all n≥15,n≡0(mod 3)with possible exception that n=*** this paper,it is shown that(i)an FSOMTS(2~n)exists if and only if n≡0,1(mod 3)and n5 with possible exceptions n ∈{9,27,33,39};(ii)an FSOMTS(3~n)exists if and only if n≥4,with possible exceptions that n ∈{6,14,18,19}.