A255382 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.

1, 3, 9, 31, 141, 969, 11289, 265577

Offset

1,2

Comments

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.

The sequence describes the number of orbits, depending on n. The elements have been obtained through a direct computation.

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).

Links

Table of n, a(n) for n=1..8.

Elias Erdtman, Carl Jönsson, Tensor Rank, Thesis, June 2014.

Crossrefs

Sequence in context: A027040 A111063 A245116 * A089475 A351185 A299549

Adjacent sequences: A255379 A255380 A255381 * A255383 A255384 A255385

Keyword

nonn,more

Author

Svyatoslav Covanov, May 05 2015

Extensions

a(8) from Svyatoslav Covanov, Oct 13 2015

Status

approved