login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A364649 Maximal number of pairwise non-orthogonal 1-dimensional subspaces over F_3^n. 0
1, 2, 5, 7, 11, 18, 28, 45, 82 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Let V=F_p^n be the n-dimensional vector space over the field F_p with p elements, where p is a prime. We call 1-dimensional subspaces <u> and <v> non-orthogonal if the standard scalar product u*v=\sum_{i=1}^n u_iv_i is nonzero. Let G be the graph with the 1-dimensional subspaces as vertices and edges given by pairs of distinct non-orthognal subspaces. It seems difficult to compute the clique number of G. For p=3, a(n) is this clique number. The given values have been computed with GAP.
LINKS
EXAMPLE
a(3)=5 by the following vectors: 100,111,112,121,122.
PROG
(GAP) LoadPackage("grape");;
p:=3;;
for n in [1..5] do
T:=Filtered(GF(p)^n, v->First(v, x->x<>0*Z(p))=Z(p)^0);; #normalized vectors
g:=Graph(Group(()), T, Permuted, {x, y}->x<>y and x*y<>0*Z(p), true);;
Print(CliqueNumber(g), "\n");
od;
CROSSREFS
Sequence in context: A338339 A224320 A247052 * A163695 A134641 A162491
KEYWORD
nonn,more
AUTHOR
Benjamin Sambale, Jul 31 2023
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 13 02:05 EDT 2024. Contains 371639 sequences. (Running on oeis4.)