Sphere-packings, lattices, and groups
Sphere-packings, lattices, and groups
Journal of Combinatorial Theory Series A
A survey on spherical designs and algebraic combinatorics on spheres
European Journal of Combinatorics
On a generalization of distance sets
Journal of Combinatorial Theory Series A
Bounds on sets with few distances
Journal of Combinatorial Theory Series A
Bounds on three- and higher-distance sets
European Journal of Combinatorics
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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