TY - JOUR
T1 - Equiangular lines and the Lemmens–Seidel conjecture
AU - Lin, Yen Chi Roger
AU - Yu, Wei Hsuan
N1 - Funding Information:
The authors thank Eiichi Bannai and Alexey Glazyrin for their helpful discussions on this work. This material is based upon work supported by the National Science Foundation, United States under Grant No. DMS-1439786 while the second author was in residence at the Institute for Computational and Experimental Research in Mathematics in Providence, RI, during the Point configurations in Geometry, Physics and Computer Science Program. Part of this work was done when the second author visited National Center for Theoretical Sciences (NCTS), Taiwan, in the summer of 2018. The authors are grateful to the support of NCTS. Finally, the authors would like to thank anonymous referees who offer useful comments on improvement of Theorem 5.3 and give clues to the remark following Theorem 5.3.
Funding Information:
The authors thank Eiichi Bannai and Alexey Glazyrin for their helpful discussions on this work. This material is based upon work supported by the National Science Foundation, United States under Grant No. DMS-1439786 while the second author was in residence at the Institute for Computational and Experimental Research in Mathematics in Providence, RI, during the Point configurations in Geometry, Physics and Computer Science Program. Part of this work was done when the second author visited National Center for Theoretical Sciences (NCTS), Taiwan, in the summer of 2018. The authors are grateful to the support of NCTS. Finally, the authors would like to thank anonymous referees who offer useful comments on improvement of Theorem 5.3 and give clues to the remark following Theorem 5.3 .
Publisher Copyright:
© 2019 Elsevier B.V.
PY - 2020/2
Y1 - 2020/2
N2 - In this paper, claims by Lemmens and Seidel in 1973 about equiangular sets of lines with angle 1∕5 are proved by carefully analyzing pillar decomposition, with the aid of the uniqueness of two-graphs on 276 vertices. The Neumann Theorem is generalized in the sense that if there are more than 2r−2 equiangular lines in Rr, then the angle is quite restricted. Together with techniques on finding saturated equiangular sets, we determine the maximum size of equiangular sets “exactly” in an r-dimensional Euclidean space for r=8, 9, and 10.
AB - In this paper, claims by Lemmens and Seidel in 1973 about equiangular sets of lines with angle 1∕5 are proved by carefully analyzing pillar decomposition, with the aid of the uniqueness of two-graphs on 276 vertices. The Neumann Theorem is generalized in the sense that if there are more than 2r−2 equiangular lines in Rr, then the angle is quite restricted. Together with techniques on finding saturated equiangular sets, we determine the maximum size of equiangular sets “exactly” in an r-dimensional Euclidean space for r=8, 9, and 10.
KW - Equiangular set
KW - Lemmens–Seidel
KW - Pillar methods
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UR - https://www.mendeley.com/catalogue/7ca03ffe-9d7c-3eab-9ab2-bd409cc2a7a1/
U2 - 10.1016/j.disc.2019.111667
DO - 10.1016/j.disc.2019.111667
M3 - Article
AN - SCOPUS:85072609684
VL - 343
JO - Discrete Mathematics
JF - Discrete Mathematics
SN - 0012-365X
IS - 2
M1 - 111667
ER -