Journal title
Electronic Notes in Discrete Mathematics
DOI
10.1016/j.endm.2017.06.024
Volume
61
Last updated
2024-04-23T09:05:44.103+01:00
Page
85-91
Abstract
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 Rn 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 Rn with common angle θ. Moreover, this is achievable only for θ = arccos 1 3 . 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 Rn, obtaining bounds which extend and improve a result of Blokhuis.
Symplectic ID
720849
Submitted to ORA
On
Favourite
Off
Publication type
Journal Article
Publication date
03 Aug 2017