Applied Finite Group Actions

The topic of this book is finite group actions and their use in order to approach finite unlabeled structures by defining them as orbits of finite groups of sets. Well-known examples are graphs, linear codes, chemical isomers, spin configurations, isomorphism classes of combinatorial designs etc.
This second edition is an extended version and puts more emphasis on applications to the constructive theory of finite structures. Recent progress in this field, in particular in design and coding theory, is described.
This book will be of great use to researchers and graduate students.

Texte du rabat

Written by one of the top experts in the fields of combinatorics and representation theory, this book distinguishes itself from the existing literature by its applications-oriented point of view. The second edition is extended, placing more emphasis on applications to the constructive theory of finite structures. Recent progress in this field, in particular in design and coding theory, is described.

Contenu

0. Labeled Structures.- 1. Unlabeled Structures.- 2. Enumeration of Unlabeled Structures.- 3. Enumeration by Weight.- 4. Enumeration by Stabilizer Class.- 5. Poset and Semigroup Actions.- 6. Representations.- 7. Further Applications.- 8. Permutations.- 9. Construction and Generation.- 10. Tables.- 11. Appendix.- 12. Comments and References.- References.