17 research outputs found
On hyperovals of polar spaces
We derive lower and upper bounds for the size of a hyperoval of a finite polar space of rank 3. We give a computer-free proof for the uniqueness, up to isomorphism, of the hyperoval of size 126 of H(5, 4) and prove that the near hexagon E-3 has up to isomorphism a unique full embedding into the dual polar space DH(5, 4)
On the structure of the directions not determined by a large affine point set
Given a point set in an -dimensional affine space of size
, we obtain information on the structure of the set of
directions that are not determined by , and we describe an application in
the theory of partial ovoids of certain partial geometries
Strongly regular graphs satisfying the 4-vertex condition
We survey the area of strongly regular graphs satisfying the 4-vertex
condition and find several new families. We describe a switching operation on
collinearity graphs of polar spaces that produces cospectral graphs. The
obtained graphs satisfy the 4-vertex condition if the original graph belongs to
a symplectic polar space.Comment: 19 page