Algebraic combinatorics via finite group actions:
Saved in:
| New Title: | Kerber, Adalbert Applied finite group actions |
|---|---|
| Main Author: | |
| Format: | Book |
| Language: | English |
| Published: |
Mannheim u.a.
BI-Wiss.-Verl.
1991
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 436 S. |
| ISBN: | 3411145218 |
Staff View
MARC
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| 245 | 1 | 0 | |a Algebraic combinatorics via finite group actions |c Adalbert Kerber |
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Record in the Search Index
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|---|---|
| adam_text | Contents
1 Actions 7
1.1 Actions of groups 8
1.2 Symmetry classes of mappings 14
1.3 Finite symmetric groups 21
1.4 Complete monomial groups 34
1.5 Enumeration of symmetry classes 39
1.6 The Involution Principle 47
1.7 Special symmetry classes 55
1 Weights 63
2.1 Enumeration by weight 64
2.2 Cycle indicator polynomials 70
2.3 Sums of cycle indicators, recursive methods 80
2.4 A generalization 86
2.5 The Decomposition Theorem 92
2.6 Species 99
3 Marks 109
3.1 Counting by stabilizer class 109
3.2 Tables of marks and Burnside matrices 119
3.3 Weighted enumeration by stabilizer class 127
3.4 Actions on posets, semigroups, lattices 135
3.5 Examples 141
3.6 The Burnside ring 147
4 Representations 155
4.1 Linear representations 156
4.2 Ordinary characters of finite groups 163
4.3 Representations of symmetric groups 168
2 Contents
4.4 Tableaux and matrices 182
4.5 The Determinantal Form 189
4.6 Standard bideterminants 197
5 Applications 219
5.1 Schur polynomials 220
5.2 Symmetric polynomials 225
5.3 The diagram lattice 230
5.4 Unimodality 236
5.5 The Littlewood Richardson Rule 243
5.6 The Murnaghan Nakayama Rule 254
5.7 Symmetrization and permutrization 265
5.8 Plethysm of representations 271
6 Permutations 279
6.1 Multiply transitive groups 280
6.2 Root number functions 287
6.3 Equations in groups 297
6.4 Up down sequences 302
6.5 Foulkes characters 310
6.6 Schubert polynomials 314
7 Constructions 327
7.1 Orbit evaluation 328
7.2 Transversals of symmetry classes 332
7.3 Orbits of centralizers 337
7.4 Recursion and orderly generation 341
7.5 Generating orbit representatives 347
7.6 Symmetry adapted bases 352
8 Tables 359
8.1 Tables of marks and Burnside matrices 360
8.1.1 Cyclic groups 360
8.1.2 Dihedral groups 365
8.1.3 Alternating groups 371
8.1.4 Symmetric groups 374
8.2 Characters of symmetric groups 377
8.2.1 Irreducible characters and Young characters . . 377
8.2.2 Foulkes tables 385
8.2.3 Character polynomials 387
8.3 Schubert polynomials 400
Contents 3
9 Comments and References 407
9.1 Historical remarks, books and reviews 407
9.2 Further comments 414
9.3 Suggestions for further reading 418
Index 427
|
| any_adam_object | 1 |
| author | Kerber, Adalbert 1939- |
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| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.2 |
| dewey-search | 512/.2 |
| dewey-sort | 3512 12 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV004260248 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:10:34Z |
| institution | BVB |
| isbn | 3411145218 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002649763 |
| oclc_num | 246751054 |
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| owner_facet | DE-12 DE-91G DE-BY-TUM DE-739 DE-20 DE-824 DE-29T DE-N32 DE-210 DE-384 DE-706 DE-522 DE-634 DE-188 |
| physical | 436 S. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | BI-Wiss.-Verl. |
| record_format | marc |
| spelling | Kerber, Adalbert 1939- Verfasser (DE-588)121199088 aut Algebraic combinatorics via finite group actions Adalbert Kerber Mannheim u.a. BI-Wiss.-Verl. 1991 436 S. txt rdacontent n rdamedia nc rdacarrier Endliche Mathematik (DE-588)4152155-9 gnd rswk-swf Gruppenoperation (DE-588)4158467-3 gnd rswk-swf Endliche Gruppe (DE-588)4014651-0 gnd rswk-swf Abzählende Kombinatorik (DE-588)4132720-2 gnd rswk-swf Diskrete Mathematik (DE-588)4129143-8 gnd rswk-swf Abzähltheorie (DE-588)4125171-4 gnd rswk-swf Diskrete Mathematik (DE-588)4129143-8 s Abzähltheorie (DE-588)4125171-4 s Gruppenoperation (DE-588)4158467-3 s DE-604 Abzählende Kombinatorik (DE-588)4132720-2 s Endliche Gruppe (DE-588)4014651-0 s Endliche Mathematik (DE-588)4152155-9 s 2. Aufl. u.d.T. Kerber, Adalbert Applied finite group actions HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002649763&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kerber, Adalbert 1939- Algebraic combinatorics via finite group actions Endliche Mathematik (DE-588)4152155-9 gnd Gruppenoperation (DE-588)4158467-3 gnd Endliche Gruppe (DE-588)4014651-0 gnd Abzählende Kombinatorik (DE-588)4132720-2 gnd Diskrete Mathematik (DE-588)4129143-8 gnd Abzähltheorie (DE-588)4125171-4 gnd |
| subject_GND | (DE-588)4152155-9 (DE-588)4158467-3 (DE-588)4014651-0 (DE-588)4132720-2 (DE-588)4129143-8 (DE-588)4125171-4 |
| title | Algebraic combinatorics via finite group actions |
| title_auth | Algebraic combinatorics via finite group actions |
| title_exact_search | Algebraic combinatorics via finite group actions |
| title_full | Algebraic combinatorics via finite group actions Adalbert Kerber |
| title_fullStr | Algebraic combinatorics via finite group actions Adalbert Kerber |
| title_full_unstemmed | Algebraic combinatorics via finite group actions Adalbert Kerber |
| title_new | Kerber, Adalbert Applied finite group actions |
| title_short | Algebraic combinatorics via finite group actions |
| title_sort | algebraic combinatorics via finite group actions |
| topic | Endliche Mathematik (DE-588)4152155-9 gnd Gruppenoperation (DE-588)4158467-3 gnd Endliche Gruppe (DE-588)4014651-0 gnd Abzählende Kombinatorik (DE-588)4132720-2 gnd Diskrete Mathematik (DE-588)4129143-8 gnd Abzähltheorie (DE-588)4125171-4 gnd |
| topic_facet | Endliche Mathematik Gruppenoperation Endliche Gruppe Abzählende Kombinatorik Diskrete Mathematik Abzähltheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002649763&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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