Erdős-Ko-Rado theorems: algebraic approaches / Christopher Godsil, University of Waterloo, Ontario, Canada ; Karen Meagher, University of Regina, Saskatchewan, Canada.
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 Theor...
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Full Text (via Cambridge) |
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| Main Authors: | , |
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge :
Cambridge University Press,
2016.
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| Series: | Cambridge studies in advanced mathematics ;
no. 149. |
| Subjects: |
MARC
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| 100 | 1 | |a Godsil, Christopher, |e author. | |
| 245 | 1 | 0 | |a Erdős-Ko-Rado theorems: algebraic approaches / |c Christopher Godsil, University of Waterloo, Ontario, Canada ; Karen Meagher, University of Regina, Saskatchewan, Canada. |
| 264 | 1 | |a Cambridge : |b Cambridge University Press, |c 2016. | |
| 264 | 4 | |c ©2016 | |
| 300 | |a 1 online resource (xvi, 335 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
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| 490 | 1 | |a Cambridge Studies in Advanced Mathematics ; |v no. 149 | |
| 500 | |a Title from publisher's bibliographic system (viewed on 18 Dec 2015). | ||
| 520 | |a 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. | ||
| 504 | |a Includes bibliographical references (pages 324-331) and index. | ||
| 505 | 0 | |a The Erdős-Ko-Rado theorem -- Bounds on cocliques -- Association schemes -- Distance-regular graphs -- Strongly regular graphs -- The Johnson scheme -- Polytopes -- The exact bound in the EKR theorem -- The Grassmann scheme -- The Hamming scheme -- Representation theory -- Representation theory of the symmetric group -- Orbitals -- Permutations -- Partitions -- Open problems. | |
| 588 | 0 | |a Print version record. | |
| 650 | 0 | |a Combinatorial analysis. | |
| 650 | 7 | |a Combinatorial analysis. |2 fast |0 (OCoLC)fst00868961 | |
| 700 | 1 | |a Meagher, Karen, |e author. | |
| 776 | 0 | 8 | |i Print version: |a Godsil, C.D. (Christopher David), 1949- |t Erdős-Ko-Rado theorems. |d Cambridge, United Kingdom : Cambridge University Press, 2016 |z 9781107128446 |w (OCoLC)935456305 |
| 830 | 0 | |a Cambridge studies in advanced mathematics ; |v no. 149. | |
| 856 | 4 | 0 | |u https://colorado.idm.oclc.org/login?url=https://doi.org/10.1017/CBO9781316414958 |z Full Text (via Cambridge) |
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