The goal of this thesis is to apply techniques from algebraic graph theory to finite incidence
geometry. The incidence geometries under consideration include projective spaces, polar …

Cameron-Liebler sets were originally defined as collections of lines (“line classes”) in PG (3,
q) sharing certain properties with line classes of symmetric tactical decompositions. While …

In this paper we develop non-existence results for m-ovoids in the classical polar spaces
Q−(2 r+ 1, q), W (2 r− 1, q) and H (2 r, q 2) for r> 2. In Bamberg et al.(2009) a lower bound on …

Let P be a finite classical polar space of rank d. An m-regular system with respect to (k− 1)-
dimensional projective spaces of P, 1≤ k≤ d− 1, is a set R of generators of P with the …

We construct a family of (q− 1) 2-ovoids of Q (4, q), the parabolic quadric of PG (4, q), for q≡
3 (mod 4). The existence of (q− 1) 2-ovoids of Q (4, q) was only known for q= 3, 7, or 11. Our …

Polar spaces over finite fields are fundamental in combinatorial geometry. The concept of
polar space was firstly introduced by F. Veldkamp who gave a system of 10 axioms in the …

Perfect 2-colorings of the grassmann graph of planes Page 1 Michigan Technological
University Digital Commons @ Michigan Tech Michigan Tech Publications 1-1-2020 Perfect …

We provide new proofs for the non-existence of ovoids in hyperbolic spaces of rank at least
four in even characteristic, and for the Hermitian polar space H (5, 4). We also improve the …

This thesis is concerned with the study of Delsarte designs in symmetric association
schemes, particularly in the context of finite geometry. We construct an infinite family of …

Although many abstractions of hemisystems of H (3, q 2) have been introduced since the first
infinite family was discovered by Cossidente and Penttila in 2005, none have been applied …