Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8904845 | Advances in Mathematics | 2018 | 24 Pages |
Abstract
The set of points in a metric space is called an s-distance set if pairwise distances between these points admit only s distinct values. Two-distance spherical sets with the set of scalar products {α,âα}, αâ[0,1), are called equiangular. The problem of determining the maximum size of s-distance sets in various spaces has a long history in mathematics. We suggest a new method of bounding the size of an s-distance set in compact 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 Rn, nâ¥7, is n(n+1)2 with possible exceptions for some n=(2k+1)2â3, kâN. We also prove the universal upper bound â¼23na2 for equiangular sets with α=1a and, employing this bound, prove a new upper bound on the size of equiangular sets in all dimensions. Finally, we classify all equiangular sets reaching this new bound.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Alexey Glazyrin, Wei-Hsuan Yu,