Polyhedral combinatorics of Coxeter groups:
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
2013
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| Schlagworte: | |
| Online-Zugang: | kostenfrei Inhaltsverzeichnis |
| Beschreibung: | Nebentitel: Polyedrische Kombinatorik von Coxetergruppen |
| Beschreibung: | XV, 103 S. graph. Darst. |
Internformat
MARC
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| 500 | |a Nebentitel: Polyedrische Kombinatorik von Coxetergruppen | ||
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Datensatz im Suchindex
| _version_ | 1804150619538194432 |
|---|---|
| adam_text | IMAGE 1
CONTENTS
SUMMARY VII
ZUSAMMENFASSUNG IX
ACKNOWLEDGEMENTS XI
NOTATION XV
INTRODUCTION 1
1 COXETER GROUPS AND DISCRETE GEOMETRY 5
1.1 BASIC NOTIONS ON COXETER GROUPS 5
1.2 GEOMETRIC REPRESENTATIONS OF COXETER GROUPS 7
1.3 MULTI-TRIANGULATIONS 12
2 A LATTICE FOR INFINITE COXETER GROUPS? 15
2.1 GEOMETRIES OF INFINITE ROOT SYSTEMS 16
2.2 EXTENDED WEAK ORDER OF COXETER GROUPS 18
2.3 LIMIT POINTS OF NORMALIZED ROOTS AND ISOTROPIC CONE 20
2.3.1 ROOTS AND NORMALIZED ROOTS IN RANKS 2, 3, 4, AND GENERAL SETTING .
21 2.3.2 THE LIMIT POINTS OF NORMALIZED ROOTS LIE IN THE ISOTROPIC CONE
... 25 2.4 COMPLETE ORTHOLATTICE FOR RANK 3 28
2.4.1 THE CONVEX UNION IS CLOSED FOR RANK 3 28
2.4.2 THE CONVEX UNION IS NOT CLOSED FOR RANK AT LEAST 4 34
2.5 FRACTAL DESCRIPTION OF THE LIMIT ROOTS 36
3 SUBWORD COMPLEXES IN DISCRETE GEOMETRY 39
3.1 SUBWORD COMPLEXES 40
3.2 CLUSTER COMPLEXES 41
3.3 MULTI-CLUSTER COMPLEXES 42
3.4 GENERAL RESULTS ON SPHERICAL SUBWORD COMPLEXES 49
3.4.1 FLIPS IN SPHERICAL SUBWORD COMPLEXES 49
3.4.2 ISOMORPHIC SPHERICAL SUBWORD COMPLEXES 51
3.5 PROOF OF THEOREM 3.8 52
3.6 PROOF OF THEOREM 3.4 53
3.6.1 PROOF OF CONDITION (I) 53
3.6.2 PROOF OF CONDITION (II) 56
3.7 POLYTOPALITY OF SPHERICAL SUBWORD COMPLEXES 56
XIII
HTTP://D-NB.INFO/1043079963
IMAGE 2
3.7.1 GENERALIZED ASSOCIAHEDRA 57
3.7.2 MULTI-ASSOCIAHEDRA OF TYPE A 58
3.7.3 MULTI-ASSOCIAHEDRA OF TYPE B 59
3.7.4 GENERALIZED MULTI-ASSOCIAHEDRA OF RANK 2 60
3.7.5 GENERALIZED MULTI-ASSOCIAHEDRA 60
3.8 SORTING WORDS OF THE LONGEST ELEMENT AND THE SIN-PROPERTY 61
3.9 COMMON VERTICES OF PERMUTAHEDRA AND GENERALIZED ASSOCIAHEDRA 64
3.9.1 NATURAL PARTIAL ORDER AND SINGLETONS 64
3.9.2 CYLINDRIC GRAPHS OF LONGEST WORDS AND CUTS 66
3.9.3 CYLINDRIC GRAPHS OF SORTING WORDS 72
3.9.4 FORMULAS FOR THE NUMBER OF SINGLETONS 74
3.9.5 UPPER BOUNDS 76
3.9.6 LOWER BOUNDS 82
3.9.7 ENUMERATIVE RESULTS 85
3.10 OPEN PROBLEMS 85
A SOME ROOT SYSTEMS OF RANK 3 & 4 89
B SUBWORD COMPLEX VADE-MECUM 91
DECLARATION OF AUTHORSHIP 93
INDEX 95
BIBLIOGRAPHY 97
|
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| discipline | Mathematik |
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| spelling | Labbé, Jean-Philippe Verfasser (DE-588)1037792866 aut Polyhedral combinatorics of Coxeter groups von Jean-Philippe Labbé Polyedrische Kombinatorik von Coxetergruppen 2013 XV, 103 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Nebentitel: Polyedrische Kombinatorik von Coxetergruppen Berlin, Freie Univ., Diss., 2013 Coxeter-Gruppe (DE-588)4261522-7 gnd rswk-swf Unendliche Gruppe (DE-588)4375539-2 gnd rswk-swf Diskrete Geometrie (DE-588)4130271-0 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Coxeter-Gruppe (DE-588)4261522-7 s Unendliche Gruppe (DE-588)4375539-2 s Diskrete Geometrie (DE-588)4130271-0 s DE-604 Erscheint auch als Online-Ausgabe urn:nbn:de:kobv:188-fudissthesis000000094753-2 http://www.diss.fu-berlin.de/diss/receive/FUDISS_thesis_000000094753 kostenfrei Volltext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026170890&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Labbé, Jean-Philippe Polyhedral combinatorics of Coxeter groups Coxeter-Gruppe (DE-588)4261522-7 gnd Unendliche Gruppe (DE-588)4375539-2 gnd Diskrete Geometrie (DE-588)4130271-0 gnd |
| subject_GND | (DE-588)4261522-7 (DE-588)4375539-2 (DE-588)4130271-0 (DE-588)4113937-9 |
| title | Polyhedral combinatorics of Coxeter groups |
| title_alt | Polyedrische Kombinatorik von Coxetergruppen |
| title_auth | Polyhedral combinatorics of Coxeter groups |
| title_exact_search | Polyhedral combinatorics of Coxeter groups |
| title_full | Polyhedral combinatorics of Coxeter groups von Jean-Philippe Labbé |
| title_fullStr | Polyhedral combinatorics of Coxeter groups von Jean-Philippe Labbé |
| title_full_unstemmed | Polyhedral combinatorics of Coxeter groups von Jean-Philippe Labbé |
| title_short | Polyhedral combinatorics of Coxeter groups |
| title_sort | polyhedral combinatorics of coxeter groups |
| topic | Coxeter-Gruppe (DE-588)4261522-7 gnd Unendliche Gruppe (DE-588)4375539-2 gnd Diskrete Geometrie (DE-588)4130271-0 gnd |
| topic_facet | Coxeter-Gruppe Unendliche Gruppe Diskrete Geometrie Hochschulschrift |
| url | http://www.diss.fu-berlin.de/diss/receive/FUDISS_thesis_000000094753 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026170890&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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