

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
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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 YenChi Roger Lin, Feb 20 2020 (Start):
WeiHsuan Yu and I checked up to M*(10) = 18 in our paper.
LemmensSeidel (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 FickusMixon paper mentions it.
M*(15) = M(15) = 36 is an old result.
(End)


REFERENCES

Lin, YenChi Roger, and WeiHsuan Yu. "Equiangular lines and the LemmensSeidel 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], 20152016.
P. W. H. Lemmens and J. J. Seidel, Equiangular lines, J. Algebra, 24 (1973), 494512.
Yenchi Roger Lin, WeiHsuan Yu, Equiangular lines and the LemmensSeidel conjecture, arXiv:1807.06249 [math.CO], 20182019. 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



