New bounds for spherical two-distance sets and equiangular lines
副标题：
时间：2017-12-28 来源：数学机械化重点实验室
题目： New bounds for spherical two-distance sets and equiangular lines
报告人： Wei-Hsuan Yu ( Brown University, USA)
时间地点： 2018.01.04 14:00pm N205
摘要： The set of points in a metric space is called an s-distance set if pairwise distances between these points admit only
s s distinct values. Two-distance spherical sets with the set of scalar products
a a and −a −a , are called equiangular. The problem of determining the maximal size of s s -distance sets in various spaces has a long history in mathematics. We determine a new method of bounding the size of an s s -distance set in two-point homogeneous spaces via zonal spherical functions. This method allows us to prove that the maximum size of a spherical two-distance set in n n dimension Euclidean space is n(n+1)/2 n(n+1)/2 with possible exceptions for some n=(2k+1) 2 −3 n=(2k+1)2−3 , where k k is a positive integer. We also prove the universal upper bound 2/3na 2 2/3na2 for equiangular sets with angle 1/a 1/a and, employing this bound, prove a new upper bound on the size of equiangular sets in an arbitrary dimension. Finally, we classify all equiangular sets reaching this new bound.
