Ebook: 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.

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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.

---

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.
Content:
Front Matter....Pages i-xxv
Labeled Structures....Pages 1-20
Unlabeled Structures....Pages 21-52
Enumeration of Unlabeled Structures....Pages 53-84
Enumeration by Weight....Pages 85-120
Enumeration by Stabilizer Class....Pages 121-140
Poset and Semigroup Actions....Pages 141-168
Representations....Pages 169-212
Further Applications....Pages 213-274
Permutations....Pages 275-316
Construction and Generation....Pages 317-352
Tables....Pages 353-396
Appendix....Pages 397-428
Comments and References....Pages 429-436
Back Matter....Pages 437-454

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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.
Content:
Front Matter....Pages i-xxv
Labeled Structures....Pages 1-20
Unlabeled Structures....Pages 21-52
Enumeration of Unlabeled Structures....Pages 53-84
Enumeration by Weight....Pages 85-120
Enumeration by Stabilizer Class....Pages 121-140
Poset and Semigroup Actions....Pages 141-168
Representations....Pages 169-212
Further Applications....Pages 213-274
Permutations....Pages 275-316
Construction and Generation....Pages 317-352
Tables....Pages 353-396
Appendix....Pages 397-428
Comments and References....Pages 429-436
Back Matter....Pages 437-454
....