Equiangular lines and the Lemmens–Seidel conjecture

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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.




Lin, Y. C. R., & Yu, W. H. (2020). Equiangular lines and the Lemmens–Seidel conjecture. Discrete Mathematics, 343(2). https://doi.org/10.1016/j.disc.2019.111667

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