Tight sets and m-ovoids of generalised quadrangles

@article{Bamberg2009TightSA,
  title={Tight sets and m-ovoids of generalised quadrangles},
  author={John Bamberg and Maska Law and Tim Penttila},
  journal={Combinatorica},
  year={2009},
  volume={29},
  pages={1-17}
}
The concept of a tight set of points of a generalised quadrangle was introduced by S. E. Payne in 1987, and that of an m-ovoid of a generalised quadrangle was introduced by J. A. Thas in 1989, and we unify these two concepts by defining intriguing sets of points. We prove that every intriguing set of points in a generalised quadrangle is an m-ovoid or a tight set, and we state an intersection result concerning these objects. In the classical generalised quadrangles, we construct new m-ovoids… 
On (0, α)-sets of generalized quadrangles
Weighted intriguing sets of finite generalised quadrangles
We construct and analyse interesting integer valued functions on the points of a generalised quadrangle which lie in the orthogonal complement of a principal eigenspace of the collinearity relation.
Intriguing sets in partial quadrangles
The point‐line geometry known as a partial quadrangle (introduced by Cameron in 1975) has the property that for every point/line non‐incident pair (P, ℓ), there is at most one line through P
Inequalities for regular near polygons, with applications to m-ovoids
Constructions of intriguing sets of polar spaces from field reduction and derivation
  • S. Kelly
  • Mathematics
    Des. Codes Cryptogr.
  • 2007
TLDR
A method of constructing intriguing sets of one polar space from those of another via field reduction through field reduction and an ovoid derivation of Payne and Thas is generalised.
A family of m-ovoids of parabolic quadrics
An infinite family of m-ovoids of Q(4, q)
The pseudo-hyperplanes and homogeneous pseudo-embeddings of the generalized quadrangles of order (3, t)
  • B. Bruyn
  • Mathematics
    Des. Codes Cryptogr.
  • 2013
TLDR
Using the computer algebra system GAP and invoking some theoretical relationships between pseudo-hyperplanes and pseudo-embeddings obtained in “De Bruyn (Adv Geom, to appear)”, a complete classification of all pseudo-Hyperplanes of Q is given.
...
...

References

SHOWING 1-10 OF 46 REFERENCES
Ovoids and spreads of finite classical polar spaces
LetP be a finite classical polar space of rankr, r⩾2. An ovoidO ofP is a pointset ofP, which has exactly one point in common with every totally isotropic subspace of rankr. It is proved that the
Interesting pointsets in generalized quadrangles and partial geometries
On m-ovoids of W3(q)
m-Systems of Polar Spaces
Flocks and Partial Flocks of Hyperbolic Quadrics via Root Systems
We construct three infinite families of partial flocks of sizes 12, 24 and 60 of the hyperbolic quadric of PG(3, q), for q congruent to -1 modulo 12, 24, 60 respectively, from the root systems of
Some p-Ranks Related to Orthogonal Spaces
AbstractWe determine the p-rank of the incidence matrix of hyperplanes of PG(n, pe) and points of a nondegenerate quadric. This yields new bounds for ovoids and the size of caps in finite orthogonal
The Affine Permutation Groups of Rank Three
(iii) G is an ajfine group, that is, the socle of G is a vector space V, where V s= {ZpY for some prime p and n=p ; moreover, if Go is the stabilizer of the zero vector in V then G = VG0, Go is an
Point-Line Geometries with a Generating Set that Depends on the Underlying Field
Suppose Г is a Lie incidence geometry defined over some field F having a Lie incidence geometry Г0 of the same type but defined over a subfield F0 ≤ F as a subgeometry. We investigate the following
The completion problem for partial packings
Packings (resolutions) of designs have been of interest to combinatorialists in recent years as a way of creating new designs from old ones. Line packings of projective 3-space were the first
...
...