1 August 2017
Electronic Notes in Discrete Mathematics
© 2017 Elsevier B.V. A family of lines through the origin in a Euclidean space is called equiangular if any pair of lines defines the same angle. The problem of estimating the maximum cardinality of such a family in R n was studied extensively for the last 70 years. Motivated by a question of Lemmens and Seidel from 1973, we prove that for every fixed angle θ and n sufficiently large, there are at most 2n−2 lines in R n with common angle θ. Moreover, this is achievable only for θ=arccos[Formula presented]. We also study analogous questions for k-dimensional subspaces. We discuss natural ways of defining the angle between k-dimensional subspaces and correspondingly study the maximum size of an equiangular set of k-dimensional subspaces in R n , obtaining bounds which extend and improve a result of Blokhuis.
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