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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, 54 <= a(18) <= 60, 72 <= a(19) <= 75, 90 <= a(20) <= 95, 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.

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

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.

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

G. Greaves, Equiangular line systems and switching classes containing regular graphs, Linear Algebra Appl. 536, pp. 31--51 (2018).

G. Greaves, J. H. Koolen, A. Munemasa, and F. Szollosi, Equiangular lines in Euclidean spaces, J. Combin. Theory Ser. A 138, pp. 208--235 (2016).

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 [quant-ph], 2014. See Abstract. - N. J. A. Sloane, Apr 09 2014

Blake C. Stacey, Geometric and Information-Theoretic Properties of the Hoggar Lines, arXiv preprint arXiv:1609.03075 [quant-ph], 2016.

F. Szollosi, A Remark on a Construction of D.S. Asche, Discrete Comput. Geom. (2017)

CROSSREFS

Sequence in context: A316563 A316140 A147849 * A278807 A184137 A135610

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 November 12 12:43 EST 2018. Contains 317109 sequences. (Running on oeis4.)