ON THE RIGIDITY OF SOME SPHERICAL 2-DESIGNS
ON THE RIGIDITY OF SOME SPHERICAL 2-DESIGNS
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一些球形2-设计的刚性
DOI：
10.2206/kyushumfs.47.1
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发表时间：
1993
期刊：
影响因子：
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通讯作者：
A. Sali
中科院分区：
文献类型：
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作者：
A. Sali
在本文中，我们将确定哪些三村型球面2-设计是刚性的。进一步，我们证明了SD-1中d+2点的球面2-设计是刚性的，并证明了d+2点的球面2-设计是唯一的。我们还证明了d+3点的2-设计是非刚性的。这项工作旨在阐明Bannai的猜想。Bannai[Ba2]猜想存在一个函数f(d，t)，使得如果X是SD-1中的球面t设计且|X|>；f(d，t)，则X是非刚性的。他证明了f(2，t)=2t+1。
In this note we shall determine which Mimura-type spherical 2-designs are rigid. Furthermore we show that spherical 2-designs of d + 2 points in Sd-1 are rigid by showing the spherical 2-design of d + 2 points is unique. We also establish that a 2-design of d + 3 points is non-rigid. This work is intended to shed some lights on conjectures of Bannai. Bannai conjectured [Ba2] that there exists a function f(d, t) such that if X is a spherical t-design in Sd-1 and |X| > f(d, t), than X is non-rigid. He has showed that f(2, t) = 2t + 1.