Department of Mathematics

Combinatorics and Graph Theory

  •  Wei-Hsuan Yu, MSU
  •  New bounds for equiangular lines and spherical two-distance sets
  •  01/31/2017
  •  4:10 PM - 5:00 PM
  •  C304 Wells Hall

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 {alpha, -alpha}, alpha in [0,1), are called equiangular. The problem of determining the maximal size of s-distance sets in various spaces has a long history in mathematics. We determine a new method of bounding the size of an 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 R^n is n(n+1)/2 with possible exceptions for some n = (2k+1)^2-3, k a positive integer. We also prove the universal upper bound ~ 2 n a^2/3 for equiangular sets with alpha = 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.



Department of Mathematics
Michigan State University
619 Red Cedar Road
C212 Wells Hall
East Lansing, MI 48824

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