Finite geometry intersecting algebraic combinatorics : an investigation of intersection problems related to Erdös-Ko-Rado theorems on Galois geometries with help from algebraic combinatorics

Abstract

The thesis investigates problem in finite geometry with methods from algebraic combinatorics.The results of the thesis are as follows. We improve the best known upper bound on EKR sets of generators of H(2d-1, q2), d odd, to approximately q(d-1)2+1. We classify the largest (d-t)-intersecting EKR sets of generators for t leq to c sqrt d and give non-trivial upper bounds for all such sets.We give a new bound on constant distance codes in H(2d-1, q2).We classify cross-intersecting EKR sets of generators for all finite classical polar spaces except H(2d-1, q2).In the latter case, a non-trivial upper bound is proven.We solve the MMS-conjecture for k-spaces in n-dimensional vector spaces for all $n$ and k as long as q is large.