[1]王丽,曹海涛.区组大小为3的四重单纯支架[J].南京师大学报(自然科学版),2010,33(01):11-15.
　Wang Li,Cao Haitao.Simple Kirkman Frames With Index 4[J].Journal of Nanjing Normal University(Natural Science Edition),2010,33(01):11-15.
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区组大小为3的四重单纯支架()
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《南京师大学报（自然科学版）》[ISSN:1001-4616/CN:32-1239/N]

卷:
第33卷
期数:
2010年01期
页码:
11-15
栏目:
数学
出版日期:
2010-03-20

文章信息/Info

Title:
Simple Kirkman Frames With Index 4
作者:
王丽1;  曹海涛2
1. 宿迁学院教师教育系, 江苏宿迁223800 2. 南京师范大学数学科学学院, 江苏南京210046
Author(s):
Wang Li1; Cao Haitao2
1.Department of Teacher Education,Suqian College,Suqian 223800,China 2. School of Mathematical Sciences, Nan jing Normal University, Nanjing 210046, China
关键词:
可分组设计;  单纯的;  支架
Keywords:
group divisib le design;  sim ple;  fram e
分类号:
O157.2
摘要:
一个(K,λ)支架是一个区组集可分为若干个带洞平行类的可分组设计(K,λ)-GDD(X,G,B),每一个带洞平行类为X\Gj的一个划分,其中Gj∈G.若一个(K,λ)支架的区组集中任意两个区组是不相同的,则称它是单纯的.单纯的支架对构造单纯的可分解填充设计有很重要的作用,后者可以用来构造统计学中的均匀设计.本文通过直接构造和递推构造的方法证明了组型一致的(3,4)单纯支架存在的必要条件也是充分的.
Abstract:
A (K, λ)-frame is a (K, λ)-GDD ( X, G, B) in w hich the co llection o f b locks B can be partitioned in to ho ley paralle l c lasses, each ho ley para llel c lass being a partition o fX \Gj for some Gj ∈G. A fram e is ca lled s imp le if a ll its b locks are distinc t. S imp le fram es are powe rfu l fo r the construc tion of sim ple K irkm an packing designs, w hich can be used in the construction of un iform designs in statistics. In this paper, w e sha ll use both d irec t constructions and recurs ive constructions to prove that the necessary cond itions for sim pleK irkman fram es o f type tu w ith index 4 a re a lso suff-i c ient.α

参考文献/References:

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[ 2]Fang K, Lu X, Tang Y, et a.l Constructions o f un iform designs by us ing reso lv ab le packings and cover ing s[ J]. D iscrete M ath, 2004, 274( 1 /3) : 25-40.
[ 3]CaoH, Wu Y. S im pleK irkm an frames w ith index 2 and 3[ J]. Journal of Nanjing No rm alUn ive rs ity: Natura l Sc ience Ed-i tion, 2008, 31( 1): 15-20.
[ 4] Shen H. Reso lvable two- fo ld trip le system s w ithout repeated b locks[ J]. Sc ience Bulle tin, 1988, 33( 24): 1 855-1 857.
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备注/Memo

备注/Memo:
基金项目: 国家自然科学基金( 10971101) . 通讯联系人: 曹海涛, 副教授, 研究方向: 组合设计. E-mail:caohaitao@njnu. edu. cn
更新日期/Last Update: 2013-04-08