型为g^n的MGDD_λ(3,4,ng)的存在性  

The Existence of MGDD_λ(3,4,ng)of Type g^n

作　　者：程美慧[1] 宋宏博 CHENG Meihui;SONG Hongbo(Huihua College,Hebei Normal University,Hebei Shijiazhuang 050091,China;Zhongying Primary School,Nankai District,Tianjin 300101,China)

机构地区：[1]河北师范大学汇华学院,河北石家庄050091 [2]天津市南开区中营小学,天津300101

出　　处：《河北师范大学学报（自然科学版）》2019年第4期277-281,共5页Journal of Hebei Normal University：Natural Science

基　　金：国家自然科学基金(11471096);河北省高等学校科学技术研究项目(Z2015151)

摘　　要：可分组3-设计是一类重要的组合设计,在3-平衡设计的研究过程中起着重要作用.Mendelsohn型可分组3-设计是可分组3-设计的一种有向推广形式,它在研究有向3-设计时有重要应用.研究了Mendelsohn型可分组3-设计的存在性问题,通过直接构造与递归构造相结合的方法,证明了:型为gn的MGDDλ(3,4,ng)存在的充要条件为λn(n-1)(n-2)g^3≡0(mod 4)且n≥4,除去n=5,λ≡1(mod 2),g≡1(mod 2).Group divisible 3-design is a king of important combinatorial design,which is useful in the research of 3-wise balanced designs.Mendelsohn group divisible 3-design is an ordered extension of group divisible 3-design,which is also useful in the research of ordered 3-designs.In this paper,we mainly investigate the existence of Mendelsohn group divisible 3-design.By direct and recursive constructions,we prove that there is an MGDDλ(3,4,ng)of type gnif and only ifλn(n-1)(n-2)g^3 equiv 0(mod 4)and n≥4,except for n=5,λ≡1(mod 2),g ≡1(mod 2).

关 键 词：3-平衡设计 可分组3-设计 Mendelsohn型可分组3-设计 

分 类 号：O157[理学—数学]