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%I #32 Oct 15 2015 07:19:23
%S 1,3,9,31,141,969,11289,265577
%N Number of vector spaces of dimension n generated by n X n matrices over F(2) of rank one, up to multiplication on the right by an invertible matrix and multiplication on the left by another invertible matrix.
%C Let L be the set of subspaces of dimension n included in n X n matrices over F(2), generated by matrices of rank one. GL_n X GL_n acts on elements of L. That is, if E and F are in L, E and F are in the same orbit if and only if there exists P x Q in GL_n X GL_n such that P E Q^(-1) = F.
%C The sequence describes the number of orbits, depending on n. The elements have been obtained through a direct computation.
%C Alternatively, this sequence can be seen as describing the number of orbits of tensors of order 3 of rank n in V x V x V with dim V = n and having rank-one slices. Thus the results corresponding to tensors with rank one slices given in the 4th section of the master's thesis of Elias Erdtman and Carl Jönsson can be seen as a particular case of this sequence (the case n=2).
%H Elias Erdtman, Carl Jönsson, <a href="http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-78449">Tensor Rank</a>, Thesis, June 2014.
%K nonn,more
%O 1,2
%A _Svyatoslav Covanov_, May 05 2015
%E a(8) from _Svyatoslav Covanov_, Oct 13 2015
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