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 最小kite覆盖设计的三角细相交问题 The Fine Triangle Intersection Problem for Minimum Kite Coverings 张桂芝1,2, 常彦勋1, 冯涛1 ZHANG Guizhi1,2,CHANG Yanxun1,*,FENG Tao1 1.北京交通大学数学系, 北京, 100044; 2. 呼伦贝尔学院数学科学学院, 呼伦贝尔, 内蒙古, 021008 1. Institute of Mathematics, Beijing Jiaotong University, Beijing, 100044, P. R. China;2. School of Mathematical Sciences, Hulunbuir College,Hulunbuir, Inner Mongolia, 021008, P. R. China 收稿日期: 2012-05-03 出版日期: 2013-10-25 DOI: 10.11845/sxjz.20130511
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 摘要 本文讨论了最小kite覆盖设计的三角细相交问题. 记${\rm Fin}(v)=\{(s,t):$ 存在一对具有s个公共区组 和$s+t$个公共三角形的$v ~\mbox{阶最小kite}~\mbox{覆盖设计}$. 记${\rm Adm}(v)=\{(s,t):s+t\leq b_v, s,t~\mbox{是非负整数} \}$, 其中$b_v=\lceil \frac{v(v-1)}{8rceil$. 本文证明了对于任意整数$v\equiv 0,1({\rm mod8)$且$v\geq 8$, 有${\rm Fin}(v)= {\rm Adm}(v)\setminus \{(b_v-1,0),(b_v-1,1)\}$; 对于任意整数$v\equiv 2,3,\cdots, 7({\rm mod8)$且$v\geq 4$, 有${\rm Fin}(v)={\rm Adm}(v)$. 关键词 ： kite覆盖设计,  三角相交数,  三角细相交数对 Abstract：In this article the fine triangle intersection problem for a pair of minimum kite coverings is investigated. Let ${\rm Fin}(v)=\{(s,t):$ $\exists$ a pair of minimum kite coverings of order $v$ intersecting in s blocks and $s+t$ triangles$\}$. Let ${\rm Adm}(v)=\{(s,t):\ s+t\leq b_v, s,t$ are nonnegative integers$\}$ and $b_v=\lceil \frac{v(v-1)}{8rceil$. It is established that ${\rm Fin}(v)= {\rm Adm}(v)\setminus \{(b_v-1,0),(b_v-1,1)\}$ for any integer $v\equiv 0,1({\rm mod8)$ and $v\geq 8$; ${\rm Fin}(v)={\rm Adm}(v)$ for any integer $v\equiv 2,3,\cdots,7({\rm mod8)$ and $v\geq 4$. Key words： triangle intersection    fine triangle intersection 基金资助:Supported by the Fundamental Research Funds for the Central Universities (No. 2011JBZ012, No. 2011JBM298) and NSFC (No. 61071221, No. 10901016)
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