维数不超10000的欧氏空间中2个同心球面上紧欧氏11-设计的非存在性  

Nonexistence of the Tight Euclidean 11-design on Two Concentric Spheres in R^n With n≤10000

作　　者：邱双月[1] 王欢[2] 

机构地区：[1]邯郸学院数理学院,邯郸河北056005 [2]河北师范大学数学与信息科学学院,石家庄河北050024

出　　处：《数学进展》2016年第6期899-911,共13页Advances in Mathematics（China）

基　　金：教育部博士点基金(No.20121303110005)

摘　　要：n维欧氏空间中2个同心球面上的紧欧氏11-设计的存在性问题是球面代数组合中的重要问题.本文借助结合方案、凝聚构型和Maple软件进行研究.首先计算出两个球面上点的内积所满足的方程.然后利用推广的L-R-S定理找到必要条件,即整性条件,再对其存在的可能情况进行排除.本文证明了,如果3≤n≤10000,那么n维欧氏空间中2个同心球面上的紧欧氏11-设计是不存在的.The existence of tight Euclidean 11-designs on two concentric spheres in Eu- clidean space R^n is an important problem in spherical algebraic combinatorics. We study our topic using the theory about association schemes, coherent configurations and Maple. First, we calculate the equations of the inner products of the points on the first sphere and the second sphere. Then by using the generalization of the L-R-S theorem, we obtain the necessary conditions of existence of tight Euclidean 11-designs; we remove the existent probabilities by using these necessary conditions. Finally, we show that if 3 ≤ n ≤ 10000, then there does not exist the tight Euclidean 11-design on two concentric spheres in R^n.

关 键 词：球面t-设计 欧氏t-设计 紧欧氏t-设计 距离集 

分 类 号：O157.2[理学—数学]