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Erdõs–Ko–Rado Theorems: Algebraic Approaches

$85.99 (C)

Part of Cambridge Studies in Advanced Mathematics

  • Date Published: November 2015
  • availability: Available
  • format: Hardback
  • isbn: 9781107128446

$ 85.99 (C)

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About the Authors
  • Aimed at graduate students and researchers, this fascinating text provides a comprehensive study of the Erdős–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.

    • Comprehensive look at the EKR Theorem covering many areas and techniques
    • Self-contained chapters and exercises make this text suitable for a graduate course
    • Final chapter outlines open research problems to inspire future research
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    Reviews & endorsements

    'This is an excellent book about Erdos-Ko-Rado (EKR) Theorems and how to prove them by algebraic methods … The writing style is reader-friendly, and proofs are well organized and easily followed. Also, every chapter contains Exercises and Notes, which are very useful for expanding understanding and finding further reading. The reviewer recommends this book without hesitation to all graduate students and researchers interested in combinatorics.' Norihide Tokushige, MathSciNet

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    Product details

    • Date Published: November 2015
    • format: Hardback
    • isbn: 9781107128446
    • length: 350 pages
    • dimensions: 235 x 158 x 23 mm
    • weight: 0.62kg
    • contains: 5 b/w illus. 170 exercises
    • availability: Available
  • Table of Contents

    1. The Erdős–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

  • Authors

    Christopher Godsil, University of Waterloo, Ontario
    Christopher Godsil is a professor in the Combinatorics and Optimization Department at the University of Waterloo, Ontario. He authored (with Gordon Royle) the popular textbook Algebraic Graph Theory. He started the Journal of Algebraic Combinatorics in 1992 and he serves on the editorial board of a number of other journals, including the Australasian Journal of Combinatorics and the Electronic Journal of Combinatorics.

    Karen Meagher, University of Regina, Saskatchewan, Canada
    Karen Meagher is an associate professor in the Department of Mathematics and Statistics at the University of Regina, Saskatchewan, Canada. Her research area is graph theory and discrete mathematics in which she has published around 25 journal articles.

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