利用正交几何构造 BIB 设计  

Orthogonal Geometries and the Construction of BIB Designs

作　　者：蔡天文 

机构地区：[1]上海交通大学应用数学系

出　　处：《上海交通大学学报》1991年第1期113-121,共9页Journal of Shanghai Jiaotong University

摘　　要：所谓一个BIB设计B[k,λ,v]是指一个序对(X,■),其中X 是一个v元集合,■是由X的某些k元子集(称为区组)组成的集族,使得X的每个2元子集恰好包含在λ个区组中.本文证明了特征不为2的有限域上正交几何的几个计数定理,利用它们构造了几种BIB设计,并计算出参数.A BIB design B[k,λ,v]is an ordered pair(X,B)where X is aset containing V elements and B is a collection of k-subsets(called blocks)of X such that each 2-subset of X is contained in exactly λ blocks.In thispaper,several enumeration theorems in orthogonal geometries over a finitefield with charactercstic≠2 are proved Their applications in the constructionof BIB designs are also discussed.

关 键 词：正交几何 BIB设计 区组 可迁性 

分 类 号：O157.2[理学—数学]