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A332546 a(n) is the maximal size of a set of equiangular lines of rank n. 1
1, 3, 6, 6, 10, 16, 28, 14, 18, 18, 20, 22, 26, 28, 36, 40 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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)

REFERENCES

Lin, Yen-Chi Roger, and Wei-Hsuan Yu. "Equiangular lines and the Lemmens-Seidel conjecture." Discrete Mathematics 343.2 (2020): 111667.

LINKS

Table of n, a(n) for n=1..16.

Matthew Fickus and Dustin G. Mixon, Tables of the existence of equiangular tight frames, arXiv:1504.00253 [math.FA], 2015-2016.

P. W. H. Lemmens and J. J. Seidel, Equiangular lines, J. Algebra, 24 (1973), 494-512.

Yen-chi Roger Lin, Wei-Hsuan Yu, Equiangular lines and the Lemmens-Seidel conjecture, arXiv:1807.06249 [math.CO], 2018-2019. See M*(n).

CROSSREFS

Cf. A002853.

Sequence in context: A316563 A316140 A147849 * A002853 A278807 A184137

Adjacent sequences:  A332543 A332544 A332545 * A332547 A332548 A332549

KEYWORD

nonn,more

AUTHOR

N. J. A. Sloane, Feb 21 2020

STATUS

approved

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Last modified July 5 21:00 EDT 2020. Contains 335473 sequences. (Running on oeis4.)