特征≠2的有限域上对称矩阵方程解的计数公式及其q超几何级数表达  

The Number of Solutions to the Symmetric Matrix Equation over a Finite Field of Ch.≠2 and Representation of Itsq hypergeometric Series

作　　者：魏鸿增[1] 张谊宾[1] 

机构地区：[1]河北师范大学

出　　处：《数学学报（中文版）》1997年第5期783-792,共10页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金;河北省教委科研项目

摘　　要：设Ｆｑ是特征≠２的有限域．本文利用Ｆｑ上奇异正交几何的理论，给出当Ａ，Ｂ分别是Ｆｑ上阶ｎ秩２ν＋δ和阶ｍ秩２ｓ＋γ的对称矩阵时，Ｆｑ上适合方程ＸＡＸ′＝Ｂ的秩ｋ的解Ｘ的个数和解Ｘ的个数的明显公式，并且用ｑ超几何级数简化表达解数公式．Let F q be a finite field with q elements,where q is a power of an odd prime. In this paper, using singular orthogonal goemetry over F q, we have given the number of solutions X of rank k and solutions X to the equation XAX′=B over F q, when A and B are symmetric matrices of order n, rank 2ν+δ and order m, rank 2s+γ, respectively. Finally, we have obtained simple representation of enumerational formulas using q hypergeometric series.

关 键 词：对称矩阵方程 Q超几何级数 解 计数公式 

分 类 号：O151.21[理学—数学]