Algebraic combinatorics on words:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2002
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Encyclopedia of mathematics and its applications
90 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Beschreibung: | XIII, 504 S. graph. Darst. |
| ISBN: | 0521812208 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804129212039168000 |
|---|---|
| adam_text | ENCYCLOPEDIA OF MATHEMATICS AND ITS APPLICATIONS ALGEBRAIC CPMBINATORICS
ON WORDS M. LOTHAIRE CAMBRIDGE UNIVERSITY PRESS CONTENTS PREFACE IX
CHAPTER 1 FINITE AND INFINITE WORDS 1 1.0 INTRODUCTION 1 1.1 SEMIGROUPS
1 1.2 WORDS 3 1.3 AUTOMATA 12 1.4 GENERATING SERIES 22 1.5 SYMBOLIC
DYNAMICAL SYSTEMS 26 1.6 UNAVOIDABLE SETS 33 PROBLEMS 40 NOTES 44
CHAPTER 2 STURMIAN WORDS 45 2.0 - INTRODUCTION 45 2.1 EQUIVALENT
DEFINITIONS 46 2.2 STANDARD WORDS . ... . 63 2.3 STURMIAN MORPHISMS . .
83 PROBLEMS . . 101 NOTES 108 CHAPTER 3 UNAVOIDABLE PATTERNS ILL 3.0
INTRODUCTION ILL 3.1 DEFINITIONS AND BASIC PROPERTIES 112 3.2 DECIDING
AVOIDABILITY: THE ZIMIN ALGORITHM 116 3.3 AVOIDABILITY ON A FIXED
ALPHABET 123 PROBLEMS ..131 NOTES 133 VI CONTENTS CHAPTER 4 SESQUIPOWERS
135 4.0 INTRODUCTION 135 4.1 BI-IDEAL SEQUENCES 136 4.2 CANONICAL
FACTORIZATIONS *.-.--.--. ~. . 137 4.3 SESQUIPOWERS AND RECURRENCE 141
4.4 EXTENSIONS OF A THEOREM OF SHIRSHOV 144 4.5 FINITENESS CONDITIONS
FOR SEMIGROUPS 149 PROBLEMS 159 NOTES 162 CHAPTER 5 THE PLACTIC MONOID
164 5.0 INTRODUCTION 164 5.1 SCHENSTED S ALGORITHM 165 5.2 GREENE S
INVARIANTS AND THE PLACTIC MONOID 167 5.3 THE ROBINSON-SCHENSTED-KNUTH
CORRESPONDENCE ... 170 5.4 SCHUR FUNCTIONS AND THE LITTLEWOOD-RICHARDSON
RULE . 176 5.5 COPLACTIC OPERATIONS 182 5.6 CYCLAGE AND CANONICAL
EMBEDDINGS 186 PROBLEMS .-, 192 NOTES 195 CHAPTER 6 CODES 197 6.0
INTRODUCTION 197 6.1 X-FACTORIZATIONS ., 198 6.2 DEFECT 204 6.3 MORE
DEFECT 209 6.4 A THEOREM OF SCHIITZENBERGER 221 PROBLEMS 224 NOTES 227
CHAPTER 7 NUMERATION SYSTEMS 230 7.0 INTRODUCTION 230 7.1 STANDARD
REPRESENTATION OF NUMBERS 231 7.2 BETA-EXPANSIONS *. . 236 7.3
[/-REPRESENTATIONS 248 7.4 REPRESENTATION OF COMPLEX NUMBERS . . ., 257
PROBLEMS . . : . , 263 NOTES ~ 267 CONTENTS VII CHAPTER 8 PERIODICITY
269 8.0 INTRODUCTION 269 8.1 PERIODS IN A FINITE WORD 270 8.2 LOCAL
VERSUS GLOBAL PERIODICITY -283 8.3 INFINITE WORDS 294 PROBLEMS 306 NOTES
310 CHAPTER 9 CENTRALIZERS OF NONCOMMUTATIVE SERIES AND POLYNOMIALS312
9.0 INTRODUCTION 312 9.1 COHN S CENTRALIZER THEOREM 313 9.2 EUCLIDEAN
DIVISION AND PRINCIPAL RIGHT IDEALS 315 9.3 INTEGRAL CLOSURE OF THE
CENTRALIZER 316 9.4 HOMOMORPHISMS INTO K[T] 319 9.5 BERGMAN S
CENTRALIZER THEOREM 320 9.6 FREE SUBALGEBRAS AND THE DEFECT THEOREM 322
9.7 APPENDIX: SOME COMMUTATIVE ALGEBRA 324 NOTES 328 CHAPTER 10
TRANSFORMATIONS ON WORDS AND Q-CALCUIUS 330 10.0 INTRODUCTION 330 10.1
THE Q-BINOMIAL COEFFICIENTS 332 10.2 THE MACMAHON VERFAHREN 334 10.3 THE
INSERTION TECHNIQUE 337 10.4 THE (T, G)-FACTORIAL GENERATING FUNCTIONS
339 10.5 WORDS AND BIWORDS 341 10.6 COMMUTATIONS 343 10.7 THE TWO
COMMUTATIONS 345 10.8 THE MAIN ALGORITHM . . . . . 347 10.9 THE INVERSE
OF THE ALGORITHM . 349 10.10 STATISTICS ON CIRCUITS 351 10.11
STATISTICS ON WORDS AND EQUIDISTRIBUTION PROPERTIES . . . 353 PROBLEMS
355 NOTES 363 CHAPTER 11 STATISTICS ON PERMUTATIONS AND WORDS 365 11.0
INTRODUCTION ........... 365 11.1 PRELIMINARIES . . 366 11.2 WORDS
WITH A GIVEN SHAPE . **. 367 11.3 BACKSTEPS OF PERMUTATIONS WITH A GIVEN
SHAPE . . . . 369 VIII CONTENTS 11.4 INVERSIONS OF PERMUTATIONS WITH A
GIVEN SHAPE 372 11.5 LYNDON FACTORIZATION AND CYCLES OF PERMUTATIONS . .
. . 375 11.6 MAJOR INDEX OF PERMUTATIONS WITH A GIVEN CYCLIC TYPE . 378
PROBLEMS . , 381 NOTES 385 CHAPTER 12 MAKANIN S ALGORITHM 387 12.0
INTRODUCTION 387 12.1 WORDS AND WORD EQUATIONS 389 12.2 THE EXPONENT OF
PERIODICITY 400 12.3 BOUNDARY EQUATIONS 406 12.4 PROOF OF THEOREM
12.3.10 432 PROBLEMS 435 NOTES 438 CHAPTER 13 INDEPENDENT SYSTEMS OF
EQUATIONS 443 13.0 INTRODUCTION 443 13.1 SETS AND EQUATIONS 444 13.2 THE
COMPACTNESS PROPERTY 447 13.3 INDEPENDENCE OF FINITE SYSTEMS OF
EQUATIONS 453 13.4 SEMIGROUPS WITHOUT THE COMPACTNESS PROPERTY ......
458 13.5 SEMIGROUPS WITH THE COMPACTNESS PROPERTY 460 PROBLEMS 468 NOTES
470 REFERENCES 473 INDEX OF NOTATION 497 GENERAL INDEX 499
|
| any_adam_object | 1 |
| author | Lothaire, M. |
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| building | Verbundindex |
| bvnumber | BV014314368 |
| callnumber-first | Q - Science |
| callnumber-label | QA164 |
| callnumber-raw | QA164 |
| callnumber-search | QA164 |
| callnumber-sort | QA 3164 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 130 SK 170 |
| ctrlnum | (OCoLC)248042580 (DE-599)BVBBV014314368 |
| dewey-full | 511.6 511/.6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.6 511/.6 |
| dewey-search | 511.6 511/.6 |
| dewey-sort | 3511.6 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| indexdate | 2024-07-09T19:01:32Z |
| institution | BVB |
| isbn | 0521812208 |
| language | English |
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| physical | XIII, 504 S. graph. Darst. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Cambridge Univ. Press |
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| series | Encyclopedia of mathematics and its applications |
| series2 | Encyclopedia of mathematics and its applications |
| spelling | Lothaire, M. Verfasser (DE-588)129256293 aut Algebraic combinatorics on words M. Lothaire 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2002 XIII, 504 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Encyclopedia of mathematics and its applications 90 Kombinatorik - Wort <Informatik> Formale Sprache (DE-588)4017848-1 gnd rswk-swf Algebraische Kombinatorik (DE-588)4596755-6 gnd rswk-swf Algebraische Kombinatorik (DE-588)4596755-6 s Formale Sprache (DE-588)4017848-1 s DE-604 Encyclopedia of mathematics and its applications 90 (DE-604)BV000903719 90 V:DE-604 application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&doc_number=009819968&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009819968&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lothaire, M. Algebraic combinatorics on words Encyclopedia of mathematics and its applications Kombinatorik - Wort <Informatik> Formale Sprache (DE-588)4017848-1 gnd Algebraische Kombinatorik (DE-588)4596755-6 gnd |
| subject_GND | (DE-588)4017848-1 (DE-588)4596755-6 |
| title | Algebraic combinatorics on words |
| title_auth | Algebraic combinatorics on words |
| title_exact_search | Algebraic combinatorics on words |
| title_full | Algebraic combinatorics on words M. Lothaire |
| title_fullStr | Algebraic combinatorics on words M. Lothaire |
| title_full_unstemmed | Algebraic combinatorics on words M. Lothaire |
| title_short | Algebraic combinatorics on words |
| title_sort | algebraic combinatorics on words |
| topic | Kombinatorik - Wort <Informatik> Formale Sprache (DE-588)4017848-1 gnd Algebraische Kombinatorik (DE-588)4596755-6 gnd |
| topic_facet | Kombinatorik - Wort <Informatik> Formale Sprache Algebraische Kombinatorik |
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