Subsets of finite general linear groups / Alena Ernst ; Supervisors: Prof. Dr. Kai-Uwe Schmidt, Prof. Dr. Margit Rösler. Paderborn, 2025
Inhalt
- Acknowledgements
- Zusammenfassung
- Abstract
- Introduction
- Representation Theory
- Association schemes
- Definitions, examples, and properties
- Subsets of association schemes
- Hoffman bounds
- The classical Hoffman bound
- Application: classical Erdős-Ko-Rado theorems
- The weighted version of the Hoffman bound
- Application: t-intersecting families of sets
- Linear Programming
- Subsets of the symmetric group
- The association scheme of the symmetric group
- Erdős-Ko-Rado theorems
- Permutation codes
- Transitive sets
- Finite general linear groups
- Erdős-Ko-Rado theorems for finite general linear groups
- Introduction and main results
- Preparations for the proofs of the pointwise and spacewise intersection theorems
- Proof strategy
- A special invertible matrix
- Estimates on some conjugacy class sizes and character degrees
- Proofs of the pointwise intersection theorems
- Proofs of the spacewise intersection theorems
- Open Problems
- Transitive subsets of finite general linear groups
- Introduction
- Designs in finite general linear groups
- Transitive subgroups
- Transitive sets and cliques
- Existence results
- Designs, codes, and orthogonal polynomials
- Open Problem
- Index
- Bibliography