The generalised symmetric group : transitivity, designs and perfect matchings / Lukas Klawuhn ; supervisors Prof. Dr. Kai-Uwe Schmidt, Prof. Dr. Igor Burban. Paderborn, 2026
Inhalt
- Acknowledgements
- Abstract
- Zusammenfassung
- Contents
- List of Figures
- List of Tables
- 1 Introduction
- 2 Representation and Character Theory
- 3 Association Schemes
- 3.1 Definitions, Examples and Basic Results
- 3.2 Codes and Designs in Association Schemes
- 3.3 Linear Programming
- 4 Codes and Designs in the Symmetric Group
- 4.1 The Association Scheme of the Symmetric Group
- 4.2 Permutation Codes
- 4.3 Transitive Subsets of the Symmetric Group
- 5 Codes and Designs in the Generalised Symmetric Group
- 5.1 The General Method
- 5.2 Wreath Products
- 5.3 Notions of Transitivity
- 5.4 Cliques
- 5.5 Comparison of Transitivity Types
- 5.6 Designs, Codes and Orthogonal Polynomials
- 5.7 Constructions and Applications
- 5.8 Open Problems
- 6 Designs of Perfect Matchings
- 6.1 Gelfand Pairs and Association Schemes
- 6.1.1 Group Algebras
- 6.1.2 Gelfand Pairs
- 6.1.3 The Perfect Matching Association Scheme
- 6.1.4 Eigenvalues of the Perfect Matching Association Scheme
- 6.2 Designs
- 6.3 Comparison of Designs
- 6.4 Examples for Small n
- 6.5 Codes
- 6.6 Open Problems
- a Appendix
- Back Matter