03064nam 2200553 450 991048062430332120170822131512.01-4704-0516-4(CKB)3360000000465094(EBL)3114163(SSID)ssj0000889156(PQKBManifestationID)11521346(PQKBTitleCode)TC0000889156(PQKBWorkID)10876195(PQKB)11192709(MiAaPQ)EBC3114163(PPN)195417992(EXLCZ)99336000000046509420080506h20082008 uy| 0engur|n|---|||||txtccrA proof of Alon's second eigenvalue conjecture and related problems /Joel FriedmanProvidence, Rhode Island :American Mathematical Society,[2008]©20081 online resource (114 p.)Memoirs of the American Mathematical Society,0065-9266 ;number 910"Volume 195, number 910 (first of 4 numbers).""September 2008."0-8218-4280-3 Includes bibliographical references (pages 99-100).""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 Ï?[sub(fund)] for G[sub(n,d)]""; ""4. Determining Ï?[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""Memoirs of the American Mathematical Society ;no. 910.EigenvaluesElectronic books.Eigenvalues.512.9/436Friedman Joel1962-902769MiAaPQMiAaPQMiAaPQBOOK9910480624303321A proof of Alon's second eigenvalue conjecture and related problems2018100UNINA