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Erdős–Ko–Rado Theorems: Algebraic Approaches (Cambridge Studies in Advanced Mathematics, Series Number 149) - Hardcover

Book 78 of 151: Cambridge Studies in Advanced Mathematics

Godsil, Christopher; Meagher, Karen

 
9781107128446: Erdős–Ko–Rado Theorems: Algebraic Approaches (Cambridge Studies in Advanced Mathematics, Series Number 149)
Hardcover
ISBN 10: 1107128447 ISBN 13: 9781107128446
Publisher: Cambridge University Press, 2015

Synopsis

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.

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About the Authors

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 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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Publisher
Cambridge University Press
Publication date
2015
Language
English
ISBN 10 
1107128447
ISBN 13 
9781107128446
Binding
Hardcover
Edition number
1
Number of pages
350