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Bibliographische Detailangaben
Vorheriger Titel:	Kerber, Adalbert Algebraic combinatorics via finite group actions
Beteilige Person:	Kerber, Adalbert 1939- (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Berlin ; Heidelberg ; New York Springer 1999
Ausgabe:	2nd, revised and expanded edition
Schriftenreihe:	Algorithms and combinatorics 19
Schlagwörter:	Grupos finitos Semigrupos Álgebra Combinatorial analysis Finite groups Group actions (Mathematics) Endliche Gruppe Diskrete Mathematik Gruppenoperation Abzähltheorie Abzählende Kombinatorik Hochschulschrift
Links:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008676340&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Beschreibung:	Literaturverz. S. 437 - 444
Umfang:	xxv, 454 Seiten Diagramme
ISBN:	3540659412 9783540659419

Internformat

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Datensatz im Suchindex

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adam_text	Table of Contents Preface to the Second Edition vii Preface to the First Edition ix List of Symbols xv 0. Labeled Structures 1 0.1 Species of Structures 2 0.2 Sum and Product of Species 10 0.3 Partitional Composition 13 0.4 Derivation, Pointing, Functorial Composition 16 0.5 The Ring of Isomorphism Classes of Species 19 1. Unlabeled Structures 21 1.1 Group Actions 21 1.2 Orbits, Cosets and Double Cosets 29 1.3 Symmetry Classes of Mappings 36 1.4 Invariant Relations 45 1.5 Hidden Symmetries 50 2. Enumeration of Unlabeled Structures 53 2.1 The Number of Orbits 53 2.2 Enumeration of Symmetry Classes 59 2.3 Application to Incidence Structures 67 2.4 Special Symmetry Classes 73 3. Enumeration by Weight 85 3.1 Weight Functions 85 3.2 Cycle Indicator Polynomials 91 3.3 Sums of Cycle Indicators, Recursive Methods 100 3.4 Applications to Chemistry 103 3.5 A Generalization 109 3.6 The Decomposition Theorem 115 xii Table of Contents 4. Enumeration by Stabilizer Class 121 4.1 Counting by Stabilizer Class 121 4.2 Asymmetric Orbits, Lyndon Words, the Cyclotomic Identity 126 4.3 Tables of Marks and Burnside Matrices 131 4.4 Weighted Enumeration by Stabilizer Class 137 5. Poset and Semigroup Actions 141 5.1 Actions on Posets, Semigroups, Lattices 141 5.2 Examples 150 5.3 Application to Combinatorial Designs 157 5.4 The Burnside Ring 162 6. Representations 169 6.1 Representations of Symmetric Groups 169 6.2 Tableaux and Matrices 181 6.3 The Determinantal Form 187 6.4 Standard Bideterminants 194 7. Further Applications 213 7.1 Schur Polynomials 213 7.2 Symmetric Polynomials 219 7.3 The Diagram Lattice 223 7.4 Unimodality 228 7.5 The Littlewood Richardson Rule 236 7.6 The Murnaghan Nakayama Rule 247 7.7 Symmetrization and Permutrization 255 7.8 Plethysm of Representations 260 7.9 Actions on Chains 267 8. Permutations 275 8.1 Multiply Transitive Groups 275 8.2 Root Number Functions 284 8.3 Equations in Groups 293 8.4 Up Down Sequences 297 8.5 Foulkes Characters 303 8.6 Schubert Polynomials 307 9. Construction and Generation 317 9.1 Orbit Evaluation 318 9.2 Transversals of Symmetry Classes 321 9.3 Orbits of Centralizers 326 9.4 The Homomorphism Principle 329 9.5 Orderly Generation 334 9.6 Generating Orbit Representatives 337 9.7 Symmetry Adapted Bases 341 9.8 Applications of Symmetry Adapted Bases 346 Table of Contents xiii 10. Tables 353 10.1 Tables of Marks and Burnside Matrices 353 10.1.1 Cyclic Groups 354 10.1.2 Dihedral Groups 358 10.1.3 Alternating Groups 363 10.1.4 Symmetric Groups 366 10.2 Characters of Symmetric Groups 369 10.2.1 Irreducible Characters and Young Characters 369 10.2.2 Foulkes Tables 378 10.2.3 Character Polynomials 380 10.3 Schubert Polynomials 392 11. Appendix 397 11.1 Groups 397 11.2 Finite Symmetric Groups 399 11.3 Rothe Diagram and Lehmer Code 406 11.4 Linear Representations 412 11.5 Ordinary Characters of Finite Groups 418 11.6 The Mobius Inversion 424 12. Comments and References 429 12.1 Historical Remarks, Books and Review Articles 429 12.2 Further Comments 432 12.3 Suggestions for Further Reading 433 References 437 Index 445
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indexdate	2024-12-20T10:35:46Z
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isbn	3540659412 9783540659419
language	English
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physical	xxv, 454 Seiten Diagramme
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series	Algorithms and combinatorics
series2	Algorithms and combinatorics
spellingShingle	Kerber, Adalbert 1939- Applied finite group actions Algorithms and combinatorics Grupos finitos larpcal Semigrupos larpcal Álgebra larpcal Combinatorial analysis Finite groups Group actions (Mathematics) Endliche Gruppe (DE-588)4014651-0 gnd Diskrete Mathematik (DE-588)4129143-8 gnd Gruppenoperation (DE-588)4158467-3 gnd Abzähltheorie (DE-588)4125171-4 gnd Abzählende Kombinatorik (DE-588)4132720-2 gnd
subject_GND	(DE-588)4014651-0 (DE-588)4129143-8 (DE-588)4158467-3 (DE-588)4125171-4 (DE-588)4132720-2 (DE-588)4113937-9
title	Applied finite group actions
title_auth	Applied finite group actions
title_exact_search	Applied finite group actions
title_full	Applied finite group actions Adalbert Kerber
title_fullStr	Applied finite group actions Adalbert Kerber
title_full_unstemmed	Applied finite group actions Adalbert Kerber
title_old	Kerber, Adalbert Algebraic combinatorics via finite group actions
title_short	Applied finite group actions
title_sort	applied finite group actions
topic	Grupos finitos larpcal Semigrupos larpcal Álgebra larpcal Combinatorial analysis Finite groups Group actions (Mathematics) Endliche Gruppe (DE-588)4014651-0 gnd Diskrete Mathematik (DE-588)4129143-8 gnd Gruppenoperation (DE-588)4158467-3 gnd Abzähltheorie (DE-588)4125171-4 gnd Abzählende Kombinatorik (DE-588)4132720-2 gnd
topic_facet	Grupos finitos Semigrupos Álgebra Combinatorial analysis Finite groups Group actions (Mathematics) Endliche Gruppe Diskrete Mathematik Gruppenoperation Abzähltheorie Abzählende Kombinatorik Hochschulschrift
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008676340&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
volume_link	(DE-604)BV000617357
work_keys_str_mv	AT kerberadalbert appliedfinitegroupactions

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