1,720,970 research outputs found
On the Generation of Dual Polar Spaces of Symplectic Type over Finite Fields
No full textAbstractIt is demonstrated that the dual polar space of typeSp2n(q),q>2, can be generated as a geometry by[formula]points
Symplectic subspaces of symplectic Grassmannians
No full textAbstractLet V be a non-degenerate symplectic space of dimension 2n over the field F and for a natural number l<n denote by Cl(V) the incidence geometry whose points are the totally isotropic l-dimensional subspaces of V. Two points U,W of Cl(V) will be collinear when W⊂U⊥ and dim(U∩W)=l−1 and then the line on U and W will consist of all the l-dimensional subspaces of U+W which contain U∩W. The isomorphism type of this geometry is denoted by Cn,l(F). When char(F)≠2 we classify subspaces S of Cl(F) where S≅Cm,k(F)
On the Generation of Dual Polar Spaces of Unitary Type Over Finite Fields
No full textAbstractIt is demonstrated that the generating rank of the dual polar space of typeU2n(q2) is(???n2n)when q>2. It is also shown that this is equal to the embedding rank of this geometry
On the Generation of Some Dual Polar Spaces of Symplectic Type OverGF(2)
No full textAbstractIt is demonstrated that the dual polar space of typeSp(2n,2) can be generated as a geometry by λ(n) =(2n+ 1)(2n− 1+ )3points whenn= 4 and 5. In the latter case this affirmatively resolves a conjecture of Brouwer that the dimension of the universal projective embedding of this geometry is λ(5)
External flats to varieties in PG(Mn,n(GF(q)))
No full textAbstractLet M = Mn,n(q) be the space of n × n matrices over the finite field GF(q), q a prime power. For each t ≤ n a subspace Φ(t) of dimension n2 − tn is constructed which contains no nonzero matrix of rank strictly less than t + 1, and it is demonstrated that these subspaces are maximal with respect to this property
A combinatorial construction of a graph with automorphism group SO+(2n,2)
No full textAbstractA simple combinatorial construction is given which takes as its imput a regular graph of valency k such that the convex closure of two points at distance two is the complete bipartite graph K3,3 and whose output is a regular graph of valency 2k+1. It is shown that the sequence of graphs obtained by starting with the graph with one point and no edges and applying the construction recursively is the family of bipartite dual polar space of type DSO+(2n,2)
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