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A002853 Maximal size of a set of equiangular lines in n dimensions.
(Formerly M2514 N0994)
0
1, 3, 6, 6, 10, 16, 28, 28, 28, 28, 28, 28, 28 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The sequence continues: 28<=a(14)<=29, a(15)=36, 40<=a(16)<=41, 48<=a(17)<=50, 48<=a(18)<=61, 72 <= a(19) <= 76, 90 <= a(20) <= 96, a(21) = 126, a(22) = 176, a(23) = ... = a(41) = 276, 276<=a(42)<=288, a(43) = 344.

Seidel claims, without proof, that a(14)=28. This is NOT known. See Greaves, Koolen, Munemasa, and Szollosi, to appear in JCTA (2015). - Ferenc Szollosi, Aug 31 2015

REFERENCES

W. W. R. Ball and H. S. M. Coxeter, "Mathematical Recreations and Essays," 13th Ed. Dover, p. 307.

A. Barg, W.-H. Yu, New bounds for equiangular lines, Contemporary Math. vol. 625, 2014, pp. 111--121.

F. Buekenhout, ed., Handbook of Incidence Geometry, 1995, p. 884.

G. Greaves, J. H. Koolen, A. Munemasa, and F. Szollosi, Equiangular lines in Euclidean spaces, to appear in JCTA (2015).

J. J. Seidel, "Discrete non-Euclidean geometry" In Buekenhout (ed.), Handbook of Incidence Geometry, Elsevier, Amsterdam, The Nederlands (1995).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Table of n, a(n) for n=1..13.

A. Barg, W.-H. Yu, New bounds for equiangular lines, arXiv:1311.3219 [math.MG], 2014.

G. Greaves, J. H. Koolen, A. Munemasa, and F. Szollosi, Equiangular lines in Euclidean spaces, arXiv:1403.2155 [math.CO], 2014-2015, to appear in JCTA (2015).

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

G. McConnell, Some non-standard ways to generate SIC-POVMs in dimensions 2 and 3, arXiv preprint arXiv:1402.7330, 2014. See Abstract. - N. J. A. Sloane, Apr 09 2014

CROSSREFS

Sequence in context: A159787 A184161 A147849 * A184137 A135610 A157018

Adjacent sequences:  A002850 A002851 A002852 * A002854 A002855 A002856

KEYWORD

hard,nonn,nice,more

AUTHOR

N. J. A. Sloane

EXTENSIONS

Terms above a(14) removed by Ferenc Szollosi, Aug 31 2015

STATUS

approved

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Last modified February 9 18:45 EST 2016. Contains 268132 sequences.