部分几何差族的存在性  

On the Existence of Partial Geometric Difference Families

作　　者：王亚楠[1] 吕婷婷 单秀玲[1] 郭志芬 WANG Ya′nan;LYU Tingting;SHAN Xiuling;GUO Zhifen(College of Mathematical Sciences,Hebei Normal University,Hebei Shijiazhuang 050024,China;Department of Fundamental Courses,Hebei Urban and Rural Construction School,Hebei Shijiazhuang 050030,China)

机构地区：[1]河北师范大学数学科学学院,河北石家庄050024 [2]河北城乡建设学校基础部,河北石家庄050030

出　　处：《河北师范大学学报（自然科学版）》2021年第6期559-562,共4页Journal of Hebei Normal University：Natural Science

基　　金：国家自然科学基金(11871019,11771119)。

摘　　要：部分几何差族是组合设计理论中差族概念的推广.通过对部分几何差族区组结构的分析,得到了区组长为4且型为(4t,1,1)的一类部分几何差族存在的充分必要条件,并讨论二面体群及阶为2p,2p^(2),2pq的非交换群上的这类部分几何差族的存在性问题.Partial geometric difference family is an extension of difference family in combinatorial design theory.By analyzing the block structures of the partial geometric difference families,we obtain the necessary and sufficient conditions for the existence of a class of partial geometric difference families with block length four and type(4t,1,1).In addition,we discuss the existence of partial geometric difference families on the dihedral group and non-commutative groups with order 2p,2p^(2) and 2pq.

关 键 词：部分几何差族 差族 存在性 

分 类 号：O157.2[理学—数学]