Algorithmic combinatorics on partial words:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton, Fla. [u.a.]
Chapman & Hall/CRC
2008
|
| Schriftenreihe: | Discrete mathematics and its applications
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references (p. 369-378) and index. - Formerly CIP |
| Beschreibung: | 385 S. graph. Darst. |
| ISBN: | 9781420060928 1420060929 |
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Datensatz im Suchindex
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| adam_text | Titel: Algorithmic combinatorics on partial words
Autor: Blanchet-Sadri, Francine
Jahr: 2008
Contents
Preface 13
I BASICS 23
1 Preliminaries on Partial Words 25
1.1 Alphabets, letters, and words.................. 25
1.2 Partial functions and partial words .............. 27
1.3 Periodicity ............................ 30
1.4 Factorizations of partial words ................. 32
1.5 Recursion and induction on partial words........... 35
1.6 Containment and compatibility................. 36
Exercises ............................. 39
Challenging exercises ...................... 40
Programming exercises ..................... 41
Bibliographic notes ....................... 42
2 Combinatorial Properties of Partial Words 43
2.1 Conjugacy ............................ 43
2.1.1 The equation xz = zy ................. 43
2.1.2 The equation xz | zy.................. 44
2.2 Commutativity.......................... 48
2.2.1 The equation xy = yx ................. 48
2.2.2 The equation xy yx.................. 48
Exercises ............................. 56
Challenging exercises ...................... 57
Programming exercises ..................... 58
Website.............................. 59
Bibliographic notes ....................... 59
II PERIODICITY 61
3 Fine and Wilf s Theorem 63
3.1 The case of zero or one hole .................. 63
3.2 The case of two or three holes ................. 64
3.3 Special partial words ...................... 67
3.3.1 p = 1 ........................... 67
3.3.2 p 1 ........................... 71
3.4 Graphs associated with partial words ............. 73
3.5 The main result ......................... 79
3.6 Related results.......................... 82
Exercises ............................. 86
Challenging exercises ...................... 88
Programming exercises ..................... 89
Websites ............................. 90
Bibliographic notes ....................... 90
4 Critical Factorization Theorem 93
4.1 Orderings............................. 93
4.2 The zero-hole case........................ 96
4.3 The main result: First version ................. 9
4.4 The main result: Second version ................ 104
4.5 Tests ............................... Ill
Exercises ............................. 112
Challenging exercises ...................... 113
Programming exercises ..................... 114
Websites ............................. 115
Bibliographic notes ....................... 115
5 Guibas and Odlyzko s Theorem 117
5.1 The zero-hole case........................ 117
5.2 The main result ......................... 120
5.3 The algorithm .......................... 145
Exercises ............................. 151
Challenging exercises ...................... 152
Programming exercises ..................... 153
Website.............................. 153
Bibliographic notes ....................... 154
III PRIMITIVITY 155
6 Primitive Partial Words 157
6.1 Testing primitivity on partial words .............. 158
6.2 Counting primitive partial words................ 162
6.3 Exact periods .......................... 164
6.4 First counting method...................... 170
6.5 Second counting method .................... 174
6.5.1 The one-hole case .................... 178
6.5.2 The two-hole case .................... 181
6.6 Existence of primitive partial words .............. 187
Exercises ............................. 195
Challenging exercises ...................... 196
Programming exercises ..................... 196
Website.............................. 197
Bibliographie notes ....................... 197
7 Unbordered Partial Words 199
7.1 Concatenations of prefixes ................... 200
7.2 More results on concatenations of prefixes........... 207
7.3 Critical factorizations ...................... 213
7.4 Conjugates ............................ 216
Exercises ............................. 217
Challenging exercises ...................... 219
Programming exercises ..................... 220
Website.............................. 220
Bibliographic notes ....................... 221
IV CODING 223
8 Pcodes of Partial Words 225
8.1 Binary relations......................... 225
8.2 Pcodes.............................. 229
8.2.1 The class T........................ 233
8.2.2 The class Ç........................ 234
8.3 Pcodes and monoids....................... 236
8.4 Prefix and suffix orderings................... 239
8.5 Border ordering......................... 241
8.6 Commutative ordering..................... 244
8.7 Circular pcodes......................... 249
Exercises ............................. 253
Challenging exercises...................... 254
Programming exercises ..................... 254
Website.............................. 255
Bibliographic notes ....................... 255
9 Deciding the Pcode Property 257
9.1 First algorithm.......................... 257
9.2 Second algorithm........................ 264
9.2.1 Domino technique on words............... 264
9.2.2 Domino technique on partial words........... 267
Exercises .....................•....... 275
Challenging exercises...................... 276
Programming exercises..................... 277
Website......................¦....... 277
Bibliographic notes ...............•....... 277
V FURTHER TOPICS 279
10 Equations on Partial Words 281
10.1 The equation xm t yn ..................... 281
10.2 The equation x2 Î ymz..................... 287
10.3 The equation xmyn |zp.................... 290
Exercises ............................. 292
Challenging exercises ...................... 293
Programming exercises ..................... 294
Website.............................. 294
Bibliographic notes ....................... 295
11 Correlations of Partial Words 297
11.1 Binary and ternary correlations ................ 297
11.2 Characterizations of correlations ................ 299
11.3 Distributive lattices ....................... 305
11.3.1 An, is a distributive lattice............... 309
11.3.2 A^ is a distributive lattice............... 309
11.4 Irreducible period sets...................... 315
11.5 Counting correlations ...................... 318
Exercises ............................. 321
Challenging exercises ...................... 322
Programming exercises ..................... 323
Website.............................. 323
Bibliographic notes ....................... 323
12 Unavoidable Sets of Partial Words 325
12.1 Unavoidable sets......................... 325
12.2 Classifying unavoidable sets of size two ............ 328
12.3 The case where k = 1 and I = 1 ............... 330
12.4 The case where k = 1 and 1 = 2 ............... 331
12.5 Larger values of k and I..................... 339
Exercises ............................. 340
Challenging exercises ...................... 341
Programming exercises ..................... 342
Website.............................. 342
Bibliographic notes ....................... 342
Solutions to Selected Exercises 345
References 369
Index 379
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| discipline | Informatik Mathematik |
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| spelling | Blanchet-Sadri, Francine Verfasser (DE-588)136226957 aut Algorithmic combinatorics on partial words Francine Blanchet-Sadri Boca Raton, Fla. [u.a.] Chapman & Hall/CRC 2008 385 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Discrete mathematics and its applications Includes bibliographical references (p. 369-378) and index. - Formerly CIP Symbolverarbeitung (DE-588)4278565-0 gnd rswk-swf Wort Informatik (DE-588)4348610-1 gnd rswk-swf Kombinatorik (DE-588)4031824-2 gnd rswk-swf Wort Informatik (DE-588)4348610-1 s Kombinatorik (DE-588)4031824-2 s Symbolverarbeitung (DE-588)4278565-0 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020134867&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Blanchet-Sadri, Francine Algorithmic combinatorics on partial words Symbolverarbeitung (DE-588)4278565-0 gnd Wort Informatik (DE-588)4348610-1 gnd Kombinatorik (DE-588)4031824-2 gnd |
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| title | Algorithmic combinatorics on partial words |
| title_auth | Algorithmic combinatorics on partial words |
| title_exact_search | Algorithmic combinatorics on partial words |
| title_full | Algorithmic combinatorics on partial words Francine Blanchet-Sadri |
| title_fullStr | Algorithmic combinatorics on partial words Francine Blanchet-Sadri |
| title_full_unstemmed | Algorithmic combinatorics on partial words Francine Blanchet-Sadri |
| title_short | Algorithmic combinatorics on partial words |
| title_sort | algorithmic combinatorics on partial words |
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| topic_facet | Symbolverarbeitung Wort Informatik Kombinatorik |
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