Dominating sets in finite generalized quadrangles

Finite Generalized Quadrangles

Generalized quadrangles, flocks, and BLT sets

Approximately five years ago Thas observed a remarkable coincidence relating certain generalized quadrangles constructed in [Ka3] to flocks of cones and translation planes [Th] (cf. [Ka2]). While there is a rapidly growing literature concerning this connection, there as yet has been no explanation for it. This note contains an observation providing at least some kind of explanation. It also con...

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. These functions generalise the intriguing sets introduced by Bamberg et al. (Combinatorica 29(1):1–17, 2009), and they provide the extra machinery to give new proofs of old results and to establish ...

Spreads and ovoids of finite generalized quadrangles

We survey recent results on spreads and ovoids of finite generalized quadrangles. Included in the survey are results on ovoids of PG(3, q); translation ovoids of Q(4, q); characterisations of generalized quadrangles using subquadrangles and ovoids of subquadrangles; and spreads of T2(Ω).

Automorphisms and characterizations of finite generalized quadrangles

Our paper surveys some new developments in the theory of automorphisms and characterizations of finite generalized quadrangles. It is the purpose to mention important new results which did not appear in the following standard works (or surveys) on the subject: Collineations of finite generalized quadrangles (S. E. Payne, 1983), Finite Generalized Quadrangles (S. E. Payne and J. A. Thas, 1984), ...