Combinatorics, words and symbolic dynamics:
Saved in:
| Other Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2016
|
| Series: | Encyclopedia of mathematics and its applications
159 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XVIII, 475 Seiten Illustrationen, Diagramme 24 cm |
| ISBN: | 9781107077027 |
Staff View
MARC
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| 245 | 1 | 0 | |a Combinatorics, words and symbolic dynamics |c edited by Valérie Berthé, Université Paris Diderot - Paris 7, France, Michel Rigo, Université de Liège, Belgium |
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Record in the Search Index
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| adam_text | Contents
List of contributors page ix
Preface xi
Acknowledgments xix
1 Preliminaries Î
V. Berthé, M. Rigo
1.1 Conventions 1
1.2 Words 1
1.3 Morphisms 4
1.4 Languages and machines 5
1.5 Symbolic dynamics 10
2 Expansions in non-integer bases 18
M. de Vries, V. Komornik
2.1 Introduction 18
2.2 Greedy and lazy expansions 19
2.3 On the cardinality of the sets £p (x) 22
2.4 The random map Kp and infinite Bernoulli convolutions 26
2.5 Lexicographic characterisations 35
2.6 Univoque bases 39
2.7 Univoque sets 50
2.8 A two-dimensional univoque set 55
2.9 Final remarks 56
2.10 Exercises 57
3 Medieties, end-first algorithms, and the case of Rosen continued frac-
tions 59
B. Rittaud
3.1 Introduction 59
3.2 Generalities 62
3.3 Examples 68
76
82
89
92
100
101
101
102
114
120
123
123
134
143
145
146
151
151
153
157
163
167
171
175
175
176
181
186
204
211
213
213
214
215
229
Conte ni s
3.4 End-first algorithms
3.5 Medieties with k letters
3.6 An end-first algorithm for ^-medieties
3.7 Exercises
3.8 Open problems
Repetitions in words
N. Rampersad, J. Shallit
4.1 Introduction
4.2 Avoidability
4.3 Dejean’s theorem
4.4 Avoiding repetitions in arithmetic progressions
4.5 Patterns
4.6 Abelian repetitions
4.7 Enumeration
4.8 Decidability for automatic sequences
4.9 Exercises
4.10 Notes
Text redundancies
G. Badkobeh, M. Crochemore, C. S. Iliopoulos, M. Kubica
5.1 Redundancy: a versatile notion
5.2 Avoiding repetitions and repeats
5.3 Finding repetitions and runs
5.4 Finding repeats
5.5 Finding covers and seeds
5.6 Palindromes
Similarity relations on words
V. MALAYA. T. HARJU, T. KÄRKI
6.1 Introduction
6.2 Preliminaries
6.3 Coding
6.4 Relational periods
6.5 Repetitions in relational words
6.6 Exercises and problems
Synchronised automata
M- P. Béal, D. Perrin
7.1 Introduction
7.2 Definitions
7.3 V
Cernÿ’s conjecture
7.4 Road colouring
Contents vii
Cellular automata, tilings and (un)computability 241
J. Kari
8.1 Cellular automata 242
8.2 Tilings and undecidability 260
8.3 Undecidability concerning cellular automata 279
8.4 Conclusion 293
8.5 Exercises 293
Multidimensional shifts of finite type and sofic shifts 296
M. Hochman
9.1 Introduction 296
9.2 Shifts of finite type and sofic shifts 297
9.3 Basic constructions and undecidability 305
9.4 Degrees of computability 317
9.5 Slices and subdynamics of sofic shifts 326
9.6 Frequencies, word growth and periodic points 342
Linearly recursive sequences and Dynkin diagrams 359
C. Reutenauer
10.1 Introduction 359
10.2 SL2-tilings of the plane 360
10.3 £¿2-tiling associated with a bi-infinite discrete path 361
10.4 Proof of Theorem 10.3.1 363
10.5 N-rational sequences 365
10.6 N-rationality of the rays in SL,2-t ings 369
10.7 Friezes 370
10.8 Dynkin diagrams 377
10.9 Rational frieze implies Dynkin diagram 382
10.10 Rationality for Dynkin diagrams of type A and A 385
10.11 Further properties of SL2-tilings 387
10.12 The other extended Dynkin diagrams 397
10.13 Problems and conjectures 397
10.14 Exercises 398
Pseudo-randomness of a random Kronecker sequence. An instance of
dynamical analysis 401
E. Cesaratto, B. Vallee
11.1 Introduction 401
11.2 Five parameters for Kronecker sequences 404
11.3 Probabilistic models 415
11.4 Statements of the main results 417
Contents
11.5 Dynamical analysis 423
11.6 Balanced costs 430
11.7 Unbalanced costs 436
11.8 Summary of functional analysis 438
11.9 Conclusion and open problems 441
Bibliography
Notation index
General index
443
464
466
Internationally recognised researchers look at developing trends in combinatorics
with applications in the study of words and in symbolic dynamics. They explain the
important concepts, providing a clear exposition of some recent results, and emphasi
the emerging connections between these different fields. Topics include combinatoric!
on words, pattern avoidance, graph theory, tilings and theory computation,
multidimensional subshifts, discrete dynaiiu: a! systems, ergodic theory, numev ’.ion
systems, dynamical arithmetics, automata theory and synchronised words, analytic
combinatorics, continued fractions and probabilistic models. Each topic is presented
a way that links it to the main themes, but then they are also ex,rnded to repetitions in
,
^ords, similarity relations, cellular automat a, friezes and Dynkin diagrams.
The book will appeal to graduate students, research mathematicians and computer
scientists working in combinatorics, theory of computation, number theory, symbolic
dynamics, tilings and stringology. It will also interest biologists using text algoriti ns.
Valérie Berthé is a CNRS Research Director at 1.1AFA (Laboratoire d’informatique
Algorithmique: Fondements et Applications) at Université Paris Diderot - Paris 7. She
has authored 70 journal or conference papers. Her main research interests are tilings,
numeration systems, substitutive dynamical systems and symbolic dynamics.
Michel Rigo is a full Professor in the Department of Mathematics at the Université de Liège,
Belgium, and he is Head of the research group in Discrete Mathematics. He has authored
more than 50 journal or conference papers and two books. His main research interests are
formal language theory, numeration systems and combinatorics on words.
|
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| author2 | Berthé, Valérie 1957- Rigo, Michel 1975- |
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| dewey-full | 511.6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.6 |
| dewey-search | 511.6 |
| dewey-sort | 3511.6 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| isbn | 9781107077027 |
| language | English |
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| spelling | Combinatorics, words and symbolic dynamics edited by Valérie Berthé, Université Paris Diderot - Paris 7, France, Michel Rigo, Université de Liège, Belgium Cambridge Cambridge University Press 2016 XVIII, 475 Seiten Illustrationen, Diagramme 24 cm txt rdacontent n rdamedia nc rdacarrier Encyclopedia of mathematics and its applications 159 Includes bibliographical references and index Informatik Combinatorial analysis Symbolic dynamics Computer science Kombinatorik (DE-588)4031824-2 gnd rswk-swf Kombinatorik (DE-588)4031824-2 s DE-604 Berthé, Valérie 1957- (DE-588)130150894 edt Rigo, Michel 1975- (DE-588)1099989027 edt Encyclopedia of mathematics and its applications 159 (DE-604)BV000903719 159 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028333784&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028333784&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Combinatorics, words and symbolic dynamics Encyclopedia of mathematics and its applications Informatik Combinatorial analysis Symbolic dynamics Computer science Kombinatorik (DE-588)4031824-2 gnd |
| subject_GND | (DE-588)4031824-2 |
| title | Combinatorics, words and symbolic dynamics |
| title_auth | Combinatorics, words and symbolic dynamics |
| title_exact_search | Combinatorics, words and symbolic dynamics |
| title_full | Combinatorics, words and symbolic dynamics edited by Valérie Berthé, Université Paris Diderot - Paris 7, France, Michel Rigo, Université de Liège, Belgium |
| title_fullStr | Combinatorics, words and symbolic dynamics edited by Valérie Berthé, Université Paris Diderot - Paris 7, France, Michel Rigo, Université de Liège, Belgium |
| title_full_unstemmed | Combinatorics, words and symbolic dynamics edited by Valérie Berthé, Université Paris Diderot - Paris 7, France, Michel Rigo, Université de Liège, Belgium |
| title_short | Combinatorics, words and symbolic dynamics |
| title_sort | combinatorics words and symbolic dynamics |
| topic | Informatik Combinatorial analysis Symbolic dynamics Computer science Kombinatorik (DE-588)4031824-2 gnd |
| topic_facet | Informatik Combinatorial analysis Symbolic dynamics Computer science Kombinatorik |
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