在线阅读 --自然科学版 2019年4期《型为gn的MGDDλ(3,4,ng)的存在性》
型为gn的MGDDλ(3,4,ng)的存在性--[在线阅读]
程美慧1, 宋宏博2
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
起止页码: 277--281页
DOI: 10.13763/j.cnki.jhebnu.nse.2019.04.001
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λ nn-1)(n-2)g3≡0(mod 4)且n≥4,除去n=5,λ≡1(mod 2),g≡1(mod 2).

The Existence of MGDDλ(3, 4, ng) of Type gn
CHENG Meihui1, SONG Hongbo2
1. Huihua College, Hebei Normal University, Hebei Shijiazhuang 050091, China;
2. Zhongying Primary School, Nankai District, Tianjin 300101, China
Abstract:
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 gn if and only if λ n(n-1)(n-2)g3 equiv 0(mod 4) and n ≥ 4,except for n=5,λ ≡1(mod 2),g ≡1(mod 2).

收稿日期: 2018-12-20
基金项目: 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)

参考文献:
[1]HANANI H.On Some Tactical Configurations[J].Canad J Math,1963,15:702-722.
[2]HANANI H.On Quadruple Systems[J].Canad J Math,1960,12:145-157.
[3]JI L J.On the 3BD-closed Set B3({4,5,6})[J].J Combin Des,2004,12:92-102.doi:10.1002/jcd.10067
[4]ZHANG J,ZANG Y J,TIAN Z H.The Spectrum of G-ODλ(3,4,v)[J].Graphs Combin,2017,33:1307-1319.
[5]宋宏博,Mendelsohn型四元系的存在性[D].石家庄:河北师范大学,2016.
[6]WANG J,JI L J.A Class of Group Divisible 3-designs and Their Applications[J].J Combin Des,2007,12:136-146.doi:10.1002/jcd.20182
[7]JI L J.An Improvement on H Design[J].J Combin Des,2009,17(1):25-35.
[8]MILLS W H.On the Existence of H Designs[J].Congr Numer,1990,79:129-141.