Spherical two-distance sets |
| |
Authors: | Oleg R Musin |
| |
Institution: | Department of Mathematics, University of Texas at Brownsville, 80 Fort Brown, Brownsville, TX 78520, USA |
| |
Abstract: | A set S of unit vectors in n-dimensional Euclidean space is called spherical two-distance set, if there are two numbers a and b so that the inner products of distinct vectors of S are either a or b. It is known that the largest cardinality g(n) of spherical two-distance sets does not exceed n(n+3)/2. This upper bound is known to be tight for n=2,6,22. The set of mid-points of the edges of a regular simplex gives the lower bound L(n)=n(n+1)/2 for g(n).In this paper using the so-called polynomial method it is proved that for nonnegative a+b the largest cardinality of S is not greater than L(n). For the case a+b<0 we propose upper bounds on |S| which are based on Delsarte's method. Using this we show that g(n)=L(n) for 6<n<22, 23<n<40, and g(23)=276 or 277. |
| |
Keywords: | Two-distance set Polynomial method Delsarte method |
本文献已被 ScienceDirect 等数据库收录! |
|