利用射影空间中的埃尔米特簇构作结合方案  

GEOMETRIC CONSTRUCTION OF ASSOCIATION SCHEMES FROM HERMITIAN VARIETIES IN A FINITE PROJECTIVE SPACE

作　　者：王恺顺[1] 张更生[2] 

机构地区：[1]北京师范大学数学系,北京100875 [2]河北师范大学数学系,石家庄050016

出　　处：《系统科学与数学》2003年第3期289-294,共6页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金

摘　　要：本文把N+1维射影空间看作一个N+1维仿射空间X和一个N维无穷远超平面H的并,利用埃尔米特簇把H上的点集划分为3个子集,对X中任两点a和b,如果线ab与H的交点属于第i个子集,定义a和b属于第i个结合类,我们证明上述构作是一个结合方案,并计算出其参数。n this paper, we partition a protective space of dimension N + 1 into the union of an affine space X of dimension N + 1 and a hyperplane H of dimension N at infinity. The points of the hyperplane H are partitioned into 3 subsets by hermitian variety. A pair of distinct points a, b ∈ X is denned to belong to class i if the line ab meets the subset i of the hyperplane H. We prove the above configuration is an association scheme and compute its parameters.

关 键 词：射影空间 埃尔米特簇 结合方案 仿射空间 超平面 酉群 奇异点 

分 类 号：O185[理学—数学]