A146890 a(n) is the maximal size of a set of lines in the complex n-dimensional space C^n with the property that all the subtriples of lines are pairwise congruent.

1, 4, 4, 8, 8, 12, 12, 16, 16

Offset

1,2

Comments

a(n) is also the largest integer such that the (n-1)-dimensional complex projective space CP^(n-1) contains an F-regular subset of a(n) points (n>1).

a(n)=2n if and only if there exists a skew conference matrix of order 2n.

References

B. Et-Taoui, Sur les m-uples F-reguliers dans les espaces projectifs complexes, Geom. Dedicata, 63(1996), 297-308.

B. Et-Taoui, Equiangular lines in C^r, Indag. Mathem., N.S., 11(2000), 201-207.

B. Et-Taoui, Equiangular lines in C^r (part II), Indag. Mathem., N.S., 13(2002), 483-486.

Boumediene Et-Taoui, Complex Conference Matrices, Complex Hadamard Matrices and Complex Equiangular Tight Frames, in Convexity and Discrete Geometry Including Graph Theory, pp 181-191, Springer 2016; DOI:10.1007/978-3-319-28186-5_16

Links

Table of n, a(n) for n=1..9.

Example

a(10)=a(11)=20, a(12)=a(13)=24, a(14)=a(15)=28, a(16)=a(17)=32, a(18) and a(19) are between 32 and 36.

Crossrefs

Sequence in context: A292135 A053249 A071339 * A168273 A278933 A351838

Adjacent sequences: A146887 A146888 A146889 * A146891 A146892 A146893

Keyword

nonn

Author

Boumediene Et-Taoui (boumediene.ettaoui(AT)uha.fr), Apr 16 2009

Status

approved