000			03076nam a22004453i 4500
001			EBC3114163
003			MiAaPQ
005			20240729124602.0
006			m o d |
007			cr cnu||||||||
008			240724s2008 xx o ||||0 eng d
020			_a9781470405168 _q(electronic bk.)
020			_z9780821842805
035			_a(MiAaPQ)EBC3114163
035			_a(Au-PeEL)EBL3114163
035			_a(CaPaEBR)ebr11039782
035			_a(OCoLC)922981826
040			_aMiAaPQ _beng _erda _epn _cMiAaPQ _dMiAaPQ
050		4	_aQA193 -- .F75 2008eb
082	0		_a512.9/436
100	1		_aFriedman, Joel.
245	1	0	_aProof of Alon’s Second Eigenvalue Conjecture and Related Problems.
250			_a1st ed.
264		1	_aProvidence : _bAmerican Mathematical Society, _c2008.
264		4	_c©2008.
300			_a1 online resource (114 pages)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aMemoirs of the American Mathematical Society ; _vv.195
505	0		_aIntro -- 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.
588			_aDescription based on publisher supplied metadata and other sources.
590			_aElectronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
650		0	_aEigenvalues.
655		4	_aElectronic books.
776	0	8	_iPrint version: _aFriedman, Joel _tProof of Alon’s Second Eigenvalue Conjecture and Related Problems _dProvidence : American Mathematical Society,c2008 _z9780821842805
797	2		_aProQuest (Firm)
830		0	_aMemoirs of the American Mathematical Society
856	4	0	_uhttps://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3114163 _zClick to View
999			_c69694 _d69694