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 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 and 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

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