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Equiangular lines and subspaces in Euclidean spaces

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 anal...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1016/j.endm.2017.06.024

Authors


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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
Mansfield College
Role:
Author
More from this funder
Name:
European Research Council
Funding agency for:
Keevash, P
Grant:
Consolidator Grant 647678
Publisher:
Elsevier
Journal:
Electronic Notes in Discrete Mathematics More from this journal
Volume:
61
Pages:
85-91
Publication date:
2017-08-03
DOI:
ISSN:
1571-0653
Keywords:
Pubs id:
pubs:720849
UUID:
uuid:69dff059-26d1-49e7-8773-699b73d88f13
Local pid:
pubs:720849
Source identifiers:
720849
Deposit date:
2018-04-04

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