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A332546
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a(n) is the maximal size of a set of equiangular lines of rank n.
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1
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1, 3, 6, 6, 10, 16, 28, 14, 18, 18, 20, 22, 26, 28, 36, 40
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OFFSET
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1,2
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COMMENTS
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In the literature this sequence is denoted by M*(n), and A002853(n) is called M(n). Of course M*(n) <= M(n).
Comments from Yen-Chi Roger Lin, Feb 20 2020 (Start):
Wei-Hsuan Yu and I checked up to M*(10) = 18 in our paper.
Lemmens-Seidel (1973) implies that M_{1/3}(n) = 2*n - 2 for n >= 8. Up to n=12, no other angles whose reciprocal is an odd integer are possible because of the relative bound.
For n=11, there is no conference graph of order 22 in R^11 (see Theorem 11 of Fickus and Mixon), therefore M*(11) = M_{1/3}(11) = 20.
For n=12, M*(12) = M_{1/3}(12) = 22.
For n=13, M_(1/3)*(13) = 24, but M*(13) = 26. This follows from the existence of a real equiangular tight frame (of angle arccos 1/5) in R^13. Table 3 of the same Fickus-Mixon paper mentions it.
M*(15) = M(15) = 36 is an old result.
(End)
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REFERENCES
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Lin, Yen-Chi Roger, and Wei-Hsuan Yu. "Equiangular lines and the Lemmens-Seidel conjecture." Discrete Mathematics 343.2 (2020): 111667.
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LINKS
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P. W. H. Lemmens and J. J. Seidel, Equiangular lines, J. Algebra, 24 (1973), 494-512.
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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