Generalized noncrossing partitions and combinatorics of coxeter groups:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, R.I.
American Math. Soc.
2009
|
| Series: | Memoirs of the American Mathematical Society
949 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Revision of the author's thesis (Ph.D.)--Cornell University, 2006. -- "Volume 202, number 949 (third of 5 numbers)." Includes bibliographical references |
| Physical Description: | IX, 159 S. graph. Darst. |
| ISBN: | 9780821844908 |
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| 500 | |a Includes bibliographical references | ||
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Record in the Search Index
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| adam_text | Titel: Generalized noncrossing partitions and combinatorics of Coxeter groups
Autor: Armstrong, Drew
Jahr: 2009
Contents
Acknowledgements ix
Chapter 1. Introduction 1
1.1. Goxeter-Catalan combinatorics 1
1.2. Noncrossing motivation 6
1.3. Outline of the memoir 9
Chapter 2. Coxeter Groups and Noncrossing Partitions 13
2.1. Coxeter systems 13
2.2. Root systems 16
2.3. Reduced words and weak order 19
2.4. Absolute order 22
2.5. Shifting and local self-duality 26
2.6. Coxeter elements and noncrossing partitions 29
2.7. Invariant theory and Catalan numbers 35
Chapter 3. fc-Divisible Noncrossing Partitions 41
3.1. Minimal factorizations 41
3.2. Multichains and delta sequences 42
3.3. Definition of A:-divisible noncrossing partitions 46
3.4. Basic properties of fc-divisible noncrossing partitions 48
3.5. Fuss-Catalan and Puss-Narayana numbers 59
3.6. The iterated construction and chain enumeration 66
3.7. Shellability and Euler characteristics 72
Chapter 4. The Classical Types 81
4.1. Classical noncrossing partitions 81
4.2. The classical Kreweras complement 87
4.3. Classical fc-divisible noncrossing partitions 92
4.4. Type A 102
4.5. Type B 104
4.6. Type D 111
Chapter 5. Puss-Catalan Combinatorics 115
5.1. Nonnesting partitions 115
5.2. Cluster complexes 128
5.3. Chapoton triangles 143
5.4. Future directions 147
Bibliography 155
V
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| indexdate | 2024-07-09T22:04:54Z |
| institution | BVB |
| isbn | 9780821844908 |
| language | English |
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| physical | IX, 159 S. graph. Darst. |
| publishDate | 2009 |
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| publisher | American Math. Soc. |
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| series | Memoirs of the American Mathematical Society |
| series2 | Memoirs of the American Mathematical Society |
| spelling | Armstrong, Drew 1979- Verfasser (DE-588)139640010 aut Generalized noncrossing partitions and combinatorics of coxeter groups Drew Armstrong Providence, R.I. American Math. Soc. 2009 IX, 159 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society 949 Revision of the author's thesis (Ph.D.)--Cornell University, 2006. -- "Volume 202, number 949 (third of 5 numbers)." Includes bibliographical references Combinatorial enumeration problems Combinatorial analysis Group actions (Mathematics) Kombinatorische Analysis (DE-588)4164746-4 gnd rswk-swf Gruppenoperation (DE-588)4158467-3 gnd rswk-swf Kombinatorische Analysis (DE-588)4164746-4 s Gruppenoperation (DE-588)4158467-3 s DE-604 Memoirs of the American Mathematical Society 949 (DE-604)BV008000141 949 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018660902&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Armstrong, Drew 1979- Generalized noncrossing partitions and combinatorics of coxeter groups Memoirs of the American Mathematical Society Combinatorial enumeration problems Combinatorial analysis Group actions (Mathematics) Kombinatorische Analysis (DE-588)4164746-4 gnd Gruppenoperation (DE-588)4158467-3 gnd |
| subject_GND | (DE-588)4164746-4 (DE-588)4158467-3 |
| title | Generalized noncrossing partitions and combinatorics of coxeter groups |
| title_auth | Generalized noncrossing partitions and combinatorics of coxeter groups |
| title_exact_search | Generalized noncrossing partitions and combinatorics of coxeter groups |
| title_full | Generalized noncrossing partitions and combinatorics of coxeter groups Drew Armstrong |
| title_fullStr | Generalized noncrossing partitions and combinatorics of coxeter groups Drew Armstrong |
| title_full_unstemmed | Generalized noncrossing partitions and combinatorics of coxeter groups Drew Armstrong |
| title_short | Generalized noncrossing partitions and combinatorics of coxeter groups |
| title_sort | generalized noncrossing partitions and combinatorics of coxeter groups |
| topic | Combinatorial enumeration problems Combinatorial analysis Group actions (Mathematics) Kombinatorische Analysis (DE-588)4164746-4 gnd Gruppenoperation (DE-588)4158467-3 gnd |
| topic_facet | Combinatorial enumeration problems Combinatorial analysis Group actions (Mathematics) Kombinatorische Analysis Gruppenoperation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018660902&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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