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101 0 $aeng
135   $aur|n|---|||||
181   $ctxt
182   $cc
183   $acr
200 12$aA proof of Alon's second eigenvalue conjecture and related problems /$fJoel Friedman
210  1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d[2008]
210  4$d©2008
215   $a1 online resource (114 p.)
225 1 $aMemoirs of the American Mathematical Society,$x0065-9266 ;$vnumber 910
300   $a"Volume 195, number 910 (first of 4 numbers)."
300   $a"September 2008."
311   $a0-8218-4280-3 
320   $aIncludes bibliographical references (pages 99-100).
327   $a""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. I?»[sub(1)] of a VLG""; ""4. Shannon's Algorithm and Formal Series""; ""5. Limiting Graphs""; ""6. Irreducible Eigenvalues""; ""7. I?»[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""
327   $a""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 I??[sub(fund)] for G[sub(n,d)]""; ""4. Determining I??[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""
327   $a""Chapter 13. Finishing the G[sub(n,d)] Proof""""Chapter 14. Finishing the Proofs of the Main Theorems""; ""Chapter 15. Closing Remarks""; ""Glossary""; ""Bibliography""
410  0$aMemoirs of the American Mathematical Society ;$vno. 910.
606   $aEigenvalues
615  0$aEigenvalues.
676   $a512.9/436
700   $aFriedman$b Joel$f1962-$01617128
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910819101303321
996   $aA proof of Alon's second eigenvalue conjecture and related problems$93948172
997   $aUNINA