

A364649


Maximal number of pairwise nonorthogonal 1dimensional subspaces over F_3^n.


0




OFFSET

1,2


COMMENTS

Let V=F_p^n be the ndimensional vector space over the field F_p with p elements, where p is a prime. We call 1dimensional subspaces <u> and <v> nonorthogonal if the standard scalar product u*v=\sum_{i=1}^n u_iv_i is nonzero. Let G be the graph with the 1dimensional subspaces as vertices and edges given by pairs of distinct nonorthognal 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



KEYWORD

nonn,more


AUTHOR



STATUS

approved



