Combinatorial game theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Math. Soc.
2013
|
| Schriftenreihe: | Graduate studies in mathematics
146 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 523 S. graph. Darst. |
| ISBN: | 9780821851906 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804150581959327744 |
|---|---|
| adam_text | Titel: Combinatorial game theory
Autor: Siegel, Aaron N
Jahr: 2013
Contents
Preface xiii
Chapter I. Combinatorial Games 1
§1. Introduction 1
§2. Hackenbush: A Detailed Example 15
§3. How to Read This Book 22
§4. A Survey of the Landscape 26
Chapter II. Short Games 53
§1. The Group G 53
§2. Canonical Form 64
§3. Numbers 68
§4. Infinitesimals 82
§5. Temperature 101
§6. Reduced Canonical Form 123
§7. Atomic Weight 136
Chapter III. The Structure of G 153
§1. Hereditary Structure 153
§2. Lattice Structure 159
§3. Group Structure 167
Chapter IV. Impartial Games 179
§1. Nim Values 179
§2. Heap Games 184
x Contents
§3. Wythoff 197
§4. Generalized Sprague-Grundy Theory 207
§5. Nim Arithmetic 214
Chapter V. Misère Play 223
§1. Misère Nim 224
§2. Genus Theory 231
§3. Misère Canonical Form 242
§4. Misère Quotients 249
§5. The Structure of Finite Misère Quotients 259
§6. Partizan Misère Canonical Form 269
Chapter VI. Loopy Games 279
§1. Coping with Cycles 279
§2. Stoppers 289
§3. Simplification of Stoppers 301
§4. Sides 309
§5. Idempotents 322
Chapter VII. Temperature Theory 333
§1. Enriched Environments 334
§2. Orthodoxy 341
§3. Generalized Temperature 351
§4. Generalized Thermography 364
§5. Komaster Thermography 377
Chapter Vili. Transfinite Games 397
§1. The Group PG 398
§2. Surreal Numbers 412
§3. The Structure of Surreal Numbers 423
§4. Transfinite Nim Arithmetic 438
Appendix A. Open Problems 455
Appendix B. Mathematical Prerequisites 459
§1. Abelian Groups 459
§2. Partial Orders 462
§3. Ordinals 465
§4. Commutative Semigroups 470
Contents xi
Appendix C. A Finite Loopfree History 475
Bibliography 493
Glossary of Notation 505
Author Index 511
Index of Games 513
Index 515
|
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| dewey-full | 519.3 |
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| dewey-ones | 519 - Probabilities and applied mathematics |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| isbn | 9780821851906 |
| language | English |
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| series | Graduate studies in mathematics |
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| spelling | Siegel, Aaron N. 1977- Verfasser (DE-588)1043564284 aut Combinatorial game theory Aaron N. Siegel Providence, RI American Math. Soc. 2013 XIV, 523 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics 146 Game theory Combinatorial analysis Game theory, economics, social and behavioral sciences -- Game theory -- Combinatorial games msc Spieltheorie (DE-588)4056243-8 gnd rswk-swf Kombinatorische Analysis (DE-588)4164746-4 gnd rswk-swf Kombinatorische Analysis (DE-588)4164746-4 s Spieltheorie (DE-588)4056243-8 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-0944-9 Graduate studies in mathematics 146 (DE-604)BV009739289 146 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026143936&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Siegel, Aaron N. 1977- Combinatorial game theory Graduate studies in mathematics Game theory Combinatorial analysis Game theory, economics, social and behavioral sciences -- Game theory -- Combinatorial games msc Spieltheorie (DE-588)4056243-8 gnd Kombinatorische Analysis (DE-588)4164746-4 gnd |
| subject_GND | (DE-588)4056243-8 (DE-588)4164746-4 |
| title | Combinatorial game theory |
| title_auth | Combinatorial game theory |
| title_exact_search | Combinatorial game theory |
| title_full | Combinatorial game theory Aaron N. Siegel |
| title_fullStr | Combinatorial game theory Aaron N. Siegel |
| title_full_unstemmed | Combinatorial game theory Aaron N. Siegel |
| title_short | Combinatorial game theory |
| title_sort | combinatorial game theory |
| topic | Game theory Combinatorial analysis Game theory, economics, social and behavioral sciences -- Game theory -- Combinatorial games msc Spieltheorie (DE-588)4056243-8 gnd Kombinatorische Analysis (DE-588)4164746-4 gnd |
| topic_facet | Game theory Combinatorial analysis Game theory, economics, social and behavioral sciences -- Game theory -- Combinatorial games Spieltheorie Kombinatorische Analysis |
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