A proof of Alon's second eigenvalue conjecture and related problems:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, R.I.
American Mathematical Society
2008
|
| Series: | Memoirs of the American Mathematical Society
910 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | "Volume 195, number 910 (first of 4 numbers)." Includes bibliographical references |
| Physical Description: | VII, 100 S. graph. Darst. |
| ISBN: | 9780821842805 |
Staff View
MARC
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| 100 | 1 | |a Friedman, Joel |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a A proof of Alon's second eigenvalue conjecture and related problems |c Joel Friedman |
| 264 | 1 | |a Providence, R.I. |b American Mathematical Society |c 2008 | |
| 300 | |a VII, 100 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Memoirs of the American Mathematical Society |v 910 | |
| 500 | |a "Volume 195, number 910 (first of 4 numbers)." | ||
| 500 | |a Includes bibliographical references | ||
| 650 | 7 | |a Matemática discreta |2 larpcal | |
| 650 | 7 | |a Teoria dos grafos |2 larpcal | |
| 650 | 4 | |a Eigenvalues | |
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| 830 | 0 | |a Memoirs of the American Mathematical Society |v 910 |w (DE-604)BV008000141 |9 910 | |
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Record in the Search Index
| _version_ | 1804137982402232320 |
|---|---|
| adam_text | Contents
Chapter
1.
Introduction
Chapter
2.
Problems with the Standard Trace Method
7
1.
The Trace Method
7
2.
Limitations of the Trace Expansion
12
Chapter
3.
Background and Terminology
17
1.
Graph Terminology
17
2.
Variable-Length Graphs and Subdivisions
18
3.
λι
of a VLG
19
4.
Shannon s Algorithm and Formal Series
19
5.
Limiting Graphs
22
6.
Irreducible Eigenvalues
22
7.
λι
and Closed Walks for Infinite Graphs
24
8.
A Curious Theorem
24
Chapter
4.
Tangles
27
Chapter
5.
Walk Sums and New Types
33
1.
Walk sums
34
2.
The Loop
39
3.
Forms, Types, and New Types
40
4.
Motivation of Types and New Types
43
Chapter
6.
The Selective Trace
47
1.
The General Selective Trace
47
2.
A Lemma on Selective Walks
47
3.
Determining TfUnd for Gn,d
51
4.
Determining Tfund for
7ť„jtj, Tn>d,
and Jn,d
51
Chapter
7.
Ramanujan Functions
57
Chapter
8.
An Expansion for Some Selective Traces
59
Chapter
9.
Selective Traces In Graphs With (Without) Tangles
65
Chapter
10.
Strongly Irreducible Traces
73
Chapter
11.
A Sidestepping Lemma
77
Chapter
12.
Magnification Theorems
81
Chapter
13.
Finishing the GnA Proof
87
vi
CONTENTS
Chapter
14.
Finishing the Proofs of the Main Theorems
91
Chapter
15.
Closing Remarks
95
Glossary
97
Bibliography
99
|
| adam_txt |
Contents
Chapter
1.
Introduction
Chapter
2.
Problems with the Standard Trace Method
7
1.
The Trace Method
7
2.
Limitations of the Trace Expansion
12
Chapter
3.
Background and Terminology
17
1.
Graph Terminology
17
2.
Variable-Length Graphs and Subdivisions
18
3.
λι
of a VLG
19
4.
Shannon's Algorithm and Formal Series
19
5.
Limiting Graphs
22
6.
Irreducible Eigenvalues
22
7.
λι
and Closed Walks for Infinite Graphs
24
8.
A Curious Theorem
24
Chapter
4.
Tangles
27
Chapter
5.
Walk Sums and New Types
33
1.
Walk sums
34
2.
The Loop
39
3.
Forms, Types, and New Types
40
4.
Motivation of Types and New Types
43
Chapter
6.
The Selective Trace
47
1.
The General Selective Trace
47
2.
A Lemma on Selective Walks
47
3.
Determining TfUnd for Gn,d
51
4.
Determining Tfund for
7ť„jtj, Tn>d,
and Jn,d
51
Chapter
7.
Ramanujan Functions
57
Chapter
8.
An Expansion for Some Selective Traces
59
Chapter
9.
Selective Traces In Graphs With (Without) Tangles
65
Chapter
10.
Strongly Irreducible Traces
73
Chapter
11.
A Sidestepping Lemma
77
Chapter
12.
Magnification Theorems
81
Chapter
13.
Finishing the GnA Proof
87
vi
CONTENTS
Chapter
14.
Finishing the Proofs of the Main Theorems
91
Chapter
15.
Closing Remarks
95
Glossary
97
Bibliography
99 |
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| ctrlnum | (OCoLC)227328566 (DE-599)BVBBV035045647 |
| dewey-full | 512.9/436 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.9/436 |
| dewey-search | 512.9/436 |
| dewey-sort | 3512.9 3436 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
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| id | DE-604.BV035045647 |
| illustrated | Illustrated |
| index_date | 2024-07-02T21:54:42Z |
| indexdate | 2024-07-09T21:20:57Z |
| institution | BVB |
| isbn | 9780821842805 |
| language | English |
| lccn | 2008020746 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016714407 |
| oclc_num | 227328566 |
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| owner | DE-355 DE-BY-UBR DE-29T DE-11 DE-188 DE-83 |
| owner_facet | DE-355 DE-BY-UBR DE-29T DE-11 DE-188 DE-83 |
| physical | VII, 100 S. graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Memoirs of the American Mathematical Society |
| series2 | Memoirs of the American Mathematical Society |
| spelling | Friedman, Joel Verfasser aut A proof of Alon's second eigenvalue conjecture and related problems Joel Friedman Providence, R.I. American Mathematical Society 2008 VII, 100 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society 910 "Volume 195, number 910 (first of 4 numbers)." Includes bibliographical references Matemática discreta larpcal Teoria dos grafos larpcal Eigenvalues Regulärer Graph (DE-588)4214561-2 gnd rswk-swf Eigenwert (DE-588)4151200-5 gnd rswk-swf Regulärer Graph (DE-588)4214561-2 s Eigenwert (DE-588)4151200-5 s DE-604 Memoirs of the American Mathematical Society 910 (DE-604)BV008000141 910 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016714407&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Friedman, Joel A proof of Alon's second eigenvalue conjecture and related problems Memoirs of the American Mathematical Society Matemática discreta larpcal Teoria dos grafos larpcal Eigenvalues Regulärer Graph (DE-588)4214561-2 gnd Eigenwert (DE-588)4151200-5 gnd |
| subject_GND | (DE-588)4214561-2 (DE-588)4151200-5 |
| title | A proof of Alon's second eigenvalue conjecture and related problems |
| title_auth | A proof of Alon's second eigenvalue conjecture and related problems |
| title_exact_search | A proof of Alon's second eigenvalue conjecture and related problems |
| title_exact_search_txtP | A proof of Alon's second eigenvalue conjecture and related problems |
| title_full | A proof of Alon's second eigenvalue conjecture and related problems Joel Friedman |
| title_fullStr | A proof of Alon's second eigenvalue conjecture and related problems Joel Friedman |
| title_full_unstemmed | A proof of Alon's second eigenvalue conjecture and related problems Joel Friedman |
| title_short | A proof of Alon's second eigenvalue conjecture and related problems |
| title_sort | a proof of alon s second eigenvalue conjecture and related problems |
| topic | Matemática discreta larpcal Teoria dos grafos larpcal Eigenvalues Regulärer Graph (DE-588)4214561-2 gnd Eigenwert (DE-588)4151200-5 gnd |
| topic_facet | Matemática discreta Teoria dos grafos Eigenvalues Regulärer Graph Eigenwert |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016714407&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
| work_keys_str_mv | AT friedmanjoel aproofofalonssecondeigenvalueconjectureandrelatedproblems |