部分几何差族构作类数为3的对称结合方案  

Three-class Symmetric Association Schemes from Partial Geometric Difference Families

作　　者：曲静 温浩颖 单秀玲[2] 张迪 QU Jing;WEN Haoying;SHAN Xiuling;ZHANG Di(School of Mathematics and Science,Hebei GEO University,Shijiazhuang,Hebei,050031,P.R.China;School of Mathematical Sciences,Hebei Normal University,Shijiazhuang,Hebei,050024,P.R.China;Tianjin Jinghai District Canal School,Tianjin,301600,P.R.China)

机构地区：[1]河北地质大学数理教学部,河北石家庄050031 [2]河北师范大学数学科学学院,河北石家庄050024 [3]天津市静海区运河学校,天津301600

出　　处：《数学进展》2025年第1期61-72,共12页Advances in Mathematics(China)

基　　金：国家自然科学基金(Nos.11771119,11871019)。

摘　　要：2014年,Nowak等人给出了部分几何差族的概念.部分几何差族概念是差族概念以及部分几何差集概念的推广.部分几何差族可用于构作部分几何设计及有向强正则图.2021年,曲静和雷建国利用部分几何设计构作了类数为3的对称结合方案.在本文中我们利用部分几何差族构作类数为3的对称结合方案并给出相应的例子.特别地,我们利用给定的部分几何差族及差阵构作具有新的参数的部分几何差族,并且给出若给定的部分几何差族在本文的构作下是类数为3的对称结合方案,则具有新的参数的部分几何差族也是类数为3的对称结合方案的充分条件.In 2014,Nowak et al.introduced the notion of a partial geometric difference family,which generalizes both the classical difference family and the partial geometric difference set.It was shown that a partial geometric difference family also gives rise to a partial geometric design or directed strongly regular graph.In 2021,Qu and Lei constructed three-class symmetric association schemes from partial geometric designs.In this paper,we show that three-class symmetric association schemes can be constructed from partial geometric difference families and we find some examples to illustrate the construction.In particular,we present a construction of a new partial geometric difference family from a given partial geometric difference family and a difference matrix,and if the given partial geometric difference family gives rise to a threeclass symmetric association scheme,we give a sufficient condition for the new partial geometric difference family to be three-class symmetric association scheme.

关 键 词：结合方案 部分几何差族 部分几何差集 部分几何设计 差阵 

分 类 号：O157.2[理学—数学]