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Proof of Alon’s Second Eigenvalue Conjecture and Related Problems.

By: Material type: TextTextSeries: Memoirs of the American Mathematical SocietyPublisher: Providence : American Mathematical Society, 2008Copyright date: ©2008Edition: 1st edDescription: 1 online resource (114 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9781470405168
Subject(s): Genre/Form: Additional physical formats: Print version:: Proof of Alon’s Second Eigenvalue Conjecture and Related ProblemsDDC classification:
  • 512.9/436
LOC classification:
  • QA193 -- .F75 2008eb
Online resources:
Contents:
Intro -- Contents -- Chapter 1. Introduction -- Chapter 2. Problems with the Standard Trace Method -- 1. The Trace Method -- 2. Limitations of the Trace Expansion -- Chapter 3. Background and Terminology -- 1. Graph Terminology -- 2. Variable-Length Graphs and Subdivisions -- 3. λ[sub(1)] of a VLG -- 4. Shannon's Algorithm and Formal Series -- 5. Limiting Graphs -- 6. Irreducible Eigenvalues -- 7. λ[sub(1)] and Closed Walks for Infinite Graphs -- 8. A Curious Theorem -- Chapter 4. Tangles -- Chapter 5. Walk Sums and New Types -- 1. Walk sums -- 2. The Loop -- 3. Forms, Types, and New Types -- 4. Motivation of Types and New Types -- Chapter 6. The Selective Trace -- 1. The General Selective Trace -- 2. A Lemma on Selective Walks -- 3. Determining τ[sub(fund)] for G[sub(n,d)] -- 4. Determining τ[sub(fund)] for H[sub(n,d)], I[sub(n,d)], and J[sub(n,d)] -- Chapter 7. Ramanujan Functions -- Chapter 8. An Expansion for Some Selective Traces -- Chapter 9. Selective Traces In Graphs With (Without) Tangles -- Chapter 10. Strongly Irreducible Traces -- Chapter 11. A Sidestepping Lemma -- Chapter 12. Magnification Theorems -- Chapter 13. Finishing the G[sub(n,d)] Proof -- Chapter 14. Finishing the Proofs of the Main Theorems -- Chapter 15. Closing Remarks -- Glossary -- Bibliography.
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Intro -- Contents -- Chapter 1. Introduction -- Chapter 2. Problems with the Standard Trace Method -- 1. The Trace Method -- 2. Limitations of the Trace Expansion -- Chapter 3. Background and Terminology -- 1. Graph Terminology -- 2. Variable-Length Graphs and Subdivisions -- 3. λ[sub(1)] of a VLG -- 4. Shannon's Algorithm and Formal Series -- 5. Limiting Graphs -- 6. Irreducible Eigenvalues -- 7. λ[sub(1)] and Closed Walks for Infinite Graphs -- 8. A Curious Theorem -- Chapter 4. Tangles -- Chapter 5. Walk Sums and New Types -- 1. Walk sums -- 2. The Loop -- 3. Forms, Types, and New Types -- 4. Motivation of Types and New Types -- Chapter 6. The Selective Trace -- 1. The General Selective Trace -- 2. A Lemma on Selective Walks -- 3. Determining τ[sub(fund)] for G[sub(n,d)] -- 4. Determining τ[sub(fund)] for H[sub(n,d)], I[sub(n,d)], and J[sub(n,d)] -- Chapter 7. Ramanujan Functions -- Chapter 8. An Expansion for Some Selective Traces -- Chapter 9. Selective Traces In Graphs With (Without) Tangles -- Chapter 10. Strongly Irreducible Traces -- Chapter 11. A Sidestepping Lemma -- Chapter 12. Magnification Theorems -- Chapter 13. Finishing the G[sub(n,d)] Proof -- Chapter 14. Finishing the Proofs of the Main Theorems -- Chapter 15. Closing Remarks -- Glossary -- Bibliography.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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