Algebraic combinatorics: lectures at a Summer School in Nordfjordeid, Norway, June 2003
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| Main Authors: | , |
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| Format: | Book |
| Language: | English |
| Published: |
Berlin
Springer
[2007]
|
| Series: | Universitext
|
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | VIII, 177 Seiten Illustrationen |
| ISBN: | 9783540683759 3540683755 |
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MARC
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Record in the Search Index
| _version_ | 1805094402530476032 |
|---|---|
| adam_text |
Contents
Part I Lectures on Arrangements
Introduction
. 5
1
Algebraic Combinatorics
. 13
1.1
Chamber Counting
. 13
1.2
Ranking Patterns
. 17
1.3
Random Walks
. 19
1.4
The Orlik-Solomon Algebra
. 23
1.5
The NBC Complex
. 27
1.6
The Aomoto Complex
. 33
1.7
Combinatorial Types
. 40
1.8
Formal Connections
. 41
1.9
Multiplicities
. 43
1.10
Ideal
Invariance
. 47
1.11
Examples
. 52
1.12
Exercises
. 58
2
Applications
. 61
2.1
Topolog}-
. 61
2.2
Local System Cohomology
. 64
2.3
Resonance
. 67
2.4
Moduli Spaces
. 68
2.5
Gauss-Manin Connections
. 70
2.6
Exercises
. 76
References
. 77
VIII Contents
Part II Discrete Morse Theory and Free Resolutions
1
Introduction
. 83
1.1
Overview
. 83
1.2
Enumerative and Algebraic Invariants of Siniplicial Complexes
85
1.3
Cohen-Macaulav Simplicial Complexes
. 92
1.4
Some Open Problems in the Field
. 97
2
Basic Definitions and Examples
.107
2.1
Multigraded Free Resolutions
.107
2.2
Basics of CW-Complexes
.113
2.3
Basics of Cellular Homology
.117
2.4
Cellular Chain Complexes and Cellular Resolutions
.120
2.5
Co-Artinian Monomial Modules
.123
3
Cellular Resolution
.125
3.1
When Does a CW-Complex Support a Cellular Resolution
? . . 125
3.2
Reading off The
Betti
Numbers
.128
3.3
Examples of Cellular Resolutions
.131
4
Discrete Morse Theory
.145
4.1
Forman's Discrete Morse Theory
.146
4.2
Discrete Morse Theory for Graded CW-Complexes
.148
4.3
Minimizing Cellular Resolutions using Discrete Morse Theory
. 158
4.4
The Morse Differential
.159
References
.169
Index
.173 |
| any_adam_object | 1 |
| author | Orlik, Peter 1938- Welker, Volkmar 1964- |
| author_GND | (DE-588)113789170X (DE-588)1050862783 |
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| author_role | aut aut |
| author_sort | Orlik, Peter 1938- |
| author_variant | p o po v w vw |
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| bvnumber | BV036584456 |
| classification_rvk | SD 2003 SK 170 |
| ctrlnum | (OCoLC)180973273 (DE-599)DNB982031718 |
| dewey-full | 511.6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.6 |
| dewey-search | 511.6 |
| dewey-sort | 3511.6 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| isbn | 9783540683759 3540683755 |
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| spelling | Orlik, Peter 1938- Verfasser (DE-588)113789170X aut Algebraic combinatorics lectures at a Summer School in Nordfjordeid, Norway, June 2003 Peter Orlik, Volkmar Welker Berlin Springer [2007] © 2007 VIII, 177 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Universitext Algebraische Kombinatorik (DE-588)4596755-6 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 2003 Nordfjordeid gnd-content Algebraische Kombinatorik (DE-588)4596755-6 s DE-604 Welker, Volkmar 1964- Verfasser (DE-588)1050862783 aut text/html http://deposit.dnb.de/cgi-bin/dokserv?id=2877249&prov=M&dok_var=1&dok_ext=htm Inhaltstext Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020505297&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Orlik, Peter 1938- Welker, Volkmar 1964- Algebraic combinatorics lectures at a Summer School in Nordfjordeid, Norway, June 2003 Algebraische Kombinatorik (DE-588)4596755-6 gnd |
| subject_GND | (DE-588)4596755-6 (DE-588)1071861417 |
| title | Algebraic combinatorics lectures at a Summer School in Nordfjordeid, Norway, June 2003 |
| title_auth | Algebraic combinatorics lectures at a Summer School in Nordfjordeid, Norway, June 2003 |
| title_exact_search | Algebraic combinatorics lectures at a Summer School in Nordfjordeid, Norway, June 2003 |
| title_full | Algebraic combinatorics lectures at a Summer School in Nordfjordeid, Norway, June 2003 Peter Orlik, Volkmar Welker |
| title_fullStr | Algebraic combinatorics lectures at a Summer School in Nordfjordeid, Norway, June 2003 Peter Orlik, Volkmar Welker |
| title_full_unstemmed | Algebraic combinatorics lectures at a Summer School in Nordfjordeid, Norway, June 2003 Peter Orlik, Volkmar Welker |
| title_short | Algebraic combinatorics |
| title_sort | algebraic combinatorics lectures at a summer school in nordfjordeid norway june 2003 |
| title_sub | lectures at a Summer School in Nordfjordeid, Norway, June 2003 |
| topic | Algebraische Kombinatorik (DE-588)4596755-6 gnd |
| topic_facet | Algebraische Kombinatorik Konferenzschrift 2003 Nordfjordeid |
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