Erdős-Ko-Rado theorems : algebraic approaches
Author(s)
Bibliographic Information
Erdős-Ko-Rado theorems : algebraic approaches
（Cambridge studies in advanced mathematics, 149）
Cambridge University Press, 2016
- : hardback
Available at / 28 libraries
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science数学
: hardback/G 5492080386178
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Note
Includes bibliographical references and index
Description and Table of Contents
Description
Aimed at graduate students and researchers, this fascinating text provides a comprehensive study of the Erdos-Ko-Rado Theorem, with a focus on algebraic methods. The authors begin by discussing well-known proofs of the EKR bound for intersecting families. The natural generalization of the EKR Theorem holds for many different objects that have a notion of intersection, and the bulk of this book focuses on algebraic proofs that can be applied to these different objects. The authors introduce tools commonly used in algebraic graph theory and show how these can be used to prove versions of the EKR Theorem. Topics include association schemes, strongly regular graphs, the Johnson scheme, the Hamming scheme and the Grassmann scheme. Readers can expand their understanding at every step with the 170 end-of-chapter exercises. The final chapter discusses in detail 15 open problems, each of which would make an interesting research project.
Table of Contents
- Preface
- 1. The Erdos-Ko-Rado Theorem
- 2. Bounds on cocliques
- 3. Association schemes
- 4. Distance-regular graphs
- 5. Strongly regular graphs
- 6. The Johnson scheme
- 7. Polytopes
- 8. The exact bound
- 9. The Grassmann scheme
- 10. The Hamming scheme
- 11. Representation theory
- 12. Representations of symmetric group
- 13. Orbitals
- 14. Permutations
- 15. Partitions
- 16. Open problems
- Glossary of symbols
- Glossary of operations and relations
- References
- Index.
by "Nielsen BookData"