TY - JOUR
T1 - Equiangular lines and the Lemmens–Seidel conjecture
AU - Lin, Yen Chi Roger
AU - Yu, Wei Hsuan
N1 - 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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U2 - 10.1016/j.disc.2019.111667
DO - 10.1016/j.disc.2019.111667
M3 - Article
AN - SCOPUS:85072609684
SN - 0012-365X
VL - 343
JO - Discrete Mathematics
JF - Discrete Mathematics
IS - 2
M1 - 111667
ER -