login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

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.
0

%I #3 Mar 24 2017 14:41:44

%S 1,4,4,8,8,12,12,16,16

%N 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.

%C 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).

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

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

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

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

%D 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

%e 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.

%K nonn

%O 1,2

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