A364649 Maximal number of pairwise non-orthogonal 1-dimensional subspaces over F_3^n.

1, 2, 5, 7, 11, 18, 28, 45, 82

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

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

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

Adjacent sequences: A364646 A364647 A364648 * A364650 A364651 A364652

Keyword

nonn,more

Author

Benjamin Sambale, Jul 31 2023

Status

approved