Equiangular lines and subspaces in Euclidean spaces

Author: 

Balla, I
Dräxler, F
Keevash, P
Sudakov, B

Publication Date: 

1 August 2017

Journal: 

Electronic Notes in Discrete Mathematics

Last Updated: 

2019-04-26T22:36:30.703+01:00

Volume: 

61

DOI: 

10.1016/j.endm.2017.06.024

page: 

85-91

abstract: 

© 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.

Symplectic id: 

720849

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article