Orbits of Creative Subspaces

Orbits of Creative Subspaces

It is shown that the creative r.e. subspaces fall into infinitely many distinct elementary classes. The techniques also extend to give some new results about orbits of creative subspaces and subfields in L*(Voo) and L*(Foo) respectively. Finally within each of these new elementary classes we construct infinitely many further orbits in the automorphism group of L(V"oo).

Lattices generated by orbits of subspaces under finite singular orthogonal groups I

Let F 2ν δ l q be a 2ν δ l -dimensional vector space over the finite field Fq. In this paperwe assume that Fq is a finite field of odd characteristic, and O2ν δ l, Δ Fq the singular orthogonal groups of degree 2ν δ l over Fq. Let M be any orbit of subspaces under O2ν δ l, Δ Fq . Denote by L the set of subspaces which are intersections of subspaces in M, where we make the convention that the int...

Lattices Generated by Two Orbits of Subspaces under Finite Singular Symplectic Groups

In the paper titled “Lattices generated by two orbits of subspaces under finite classical group” byWang andGuo.The subspaces in the lattices are characterized and the geometricity is classified. In this paper, the result above is generalized to singular symplectic space. This paper characterizes the subspaces in these lattices, classifies their geometricity, and computes their characteristic po...

Comment on frame's of subspaces

Covering of subspaces by subspaces

Lower and upper bounds on the size of a covering of subspaces in the Grassmann graph Gq(n, r) by subspaces from the Grassmann graph Gq(n, k), k ≥ r , are discussed. The problem is of interest from four points of view: coding theory, combinatorial designs, q-analogs, and projective geometry. In particular we examine coverings based on lifted maximum rank distance codes, combined with spreads and...