Finite geometries

  title={Finite geometries},
  author={Aart Blokhuis and James W. P. Hirschfeld and Dieter Jungnickel and Joseph A. Thas},
  journal={Designs, Codes and Cryptography},
Oberwolfach, 2–8 December 
1 Citations



The Complete Intersection Theorem for Systems of Finite Sets

We are concerned here with one of the oldest problems in combinatorial extremal theory. It is readily described after we have made a few conventions. ‫ގ‬ denotes the set of

Half Moufang implies Moufang for finite generalized quadrangles

SummaryA finite generalized quadrangle has two types of panels. If each panel of one type is Moufang, then every panel is Moufang. Hence by a theorem of Fong and Seitz [1] the quadrangle is classical

Combinatorics of Finite Geometries

In this lecture we intend to present a brief survey of very recent results. We shall be interested in the development of some topics considered in section 3.2 of Dembowski’s book [21] (Combinatorics

New geometries for finite groups and polytopes

We describe two methods to obtain new geometries from classes of geometries whose diagram satisfy given conditions. This gives rise to lots of new geometries for finite groups, and in particular for

A categorical glimpse at the reconstruction of geometries

The author's reconstruction method [‘Reconstruction of incidence geometries from groups of automorphisms’,Arch. Math.58 (1992) 621–624] is put in a categorical setting, and generalized to geometries

Projective planes I

Blocking sets and semifields

Shult sets and translation ovoids of the Hermitian surface

Starting with carefully chosen sets of points in the Desarguesian affine plane AG(2, q2) and using an idea first formulated by E. Shult, several infinite families of translation ovoids of the

Lacunary Polynomials, Multiple Blocking Sets and Baer Subplanes

New lower bounds are given for the size of a point set in a Desarguesian projective plane over a finite field that contains at least a prescribed number s of points on every line. These bounds are

On the simple connectedness of certain subsets of buildings

Abstract We prove a rank 3 criterion for the simple connectedness of certain subsets of buildings and we give two applications of this criterion. The first generalizes a result of Tits for Chevalley