Analytic combinatorics:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2009
|
| Ausgabe: | 1. publ. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | XIII, 810 S. zahlr. graph. Darst. |
| ISBN: | 9780521898065 0521898064 |
Internformat
MARC
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| 100 | 1 | |a Flajolet, Philippe |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Analytic combinatorics |c Philippe Flajolet & Robert Sedgewick |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2009 | |
| 300 | |a XIII, 810 S. |b zahlr. graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 7 | |a Combinatieleer |2 gtt | |
| 650 | 4 | |a Combinatorial analysis | |
| 650 | 0 | 7 | |a Kombinatorische Analysis |0 (DE-588)4164746-4 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Kombinatorische Analysis |0 (DE-588)4164746-4 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Sedgewick, Robert |d 1946- |e Verfasser |0 (DE-588)112418317 |4 aut | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017063871&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-017063871 | ||
Datensatz im Suchindex
| _version_ | 1804138540184895488 |
|---|---|
| adam_text | Contents
Preface ix
An Invitation to Analytic Combinatorics 1
Part A. SYMBOLIC METHODS 13
I. Combinatorial Structures and Ordinary Generating Functions 15
I. 1. Symbolic enumeration methods 16
1.2. Admissible constructions and specifications 24
1.3. Integer compositions and partitions 39
1.4. Words and regular languages 49
1.5. Tree structures 64
1.6. Additional constructions 83
1.7. Perspective 92
II. Labelled Structures and Exponential Generating Functions 95
II. 1. Labelled classes 96
II. 2. Admissible labelled constructions 100
II. 3. Surjections. set partitions, and words 106
II. 4. Alignments, permutations, and related structures 119
II. 5. Labelled trees, mappings, and graphs 125
II. 6. Additional constructions 136
II. 7. Perspective 147
II!. Combinatorial Parameters and Multivariate Generating Functions 151
III. 1. An introduction to Divariate generating functions (BGFs) 152
III. 2. Bivariate generating functions and probability distributions 156
III. 3. Inherited parameters and ordinary MGFs 163
III. 4. Inherited parameters and exponential MGFs 174
III. 5. Recursive parameters I SI
III. 6. Complete generating functions and discrete models 186
III. 7. Additional constructions 198
III. 8. Extremal parameters 214
III. 9. Perspective 218
Part B. COMPLEX ASYMPTOTICS 221
IV. Complex Analysis. Rational and Meromorphic Asymptotics 223
IV. 1. Generating functions as anah tic objects 225
IV. 2. Analytic functions and meromorphic functions 229
vi COXTEMS
IV. 3. Singularities and exponential growth of coefficients 238
IV 4. Closure properties and computable bounds 249
IV. 5. Rational and meromorphic functions 255
IV. 6. Localization of singularities 263
IV. 7. Singularities and functional equations 275
IV. 8. Perspective 286
V. APPLICATIONS OF RATIONAL AND MEROMORPHIC ASYMPTOTICS 289
V. I. A roadmap to rational and meromorphic asymptotics 290
V. 2. The supercritical sequence schema 293
V. 3. Regular specifications and languages 300
V. 4. Nested sequences, lattice paths, and continued fractions 318
V. 5. Paths in graphs and automata 336
V. 6. Transfer matrix models 356
V. 7. Perspective 373
VI. Singularity Analysis of Generating Functions 375
. 1. A glimpse of basic singularity analysis theory 376
. 2. Coefficient asymptotics for the standard scale 380
Transfers 389
.4. The process of singularity analysis 392
.5. Multiple singularities 398
.6. Intermezzo: functions amenable to singularity analvsis 401
V
V
V
V
V
V
VI. 7. Inverse functions 402
VI. S. Poly logarithms 408
VI. 9. Functional composition 411
VI. 10. Closure properties 418
VI. I 1. Tauberian theory and Darboux s method 433
VI. 12. Perspective 437
VII. Applications of Singularity Analysis 439
VII. 1. A roadmap to singularity analysis asymptotics 441
VII. 2. Sets and the e p-log schema 445
VII. 3. Simple varieties of trees and inverse functions 452
VII. 4. Tree-like structures and implicit functions 467
VII. 5. l nlabelled non-plane trees and Pólya operators 475
VII. (1. Irreducible context-free structures 4^2
VII. ~. The general analysis of algebraic functions 493
VII. S. Combinatorial applications of algebraic functions 506
Vll.y. Ordinary differential equations and systems 51g
II. 10. Singularity analv sis and probability distributions 532
VU. I 1. Perspective 53s;
VIII. S vmh 1 -I oiN 1 asYviprones 541
III. I. Landscapes of analytic functions and saddle-points 543
VIII. 2. Saddle-point bounds 545
lll.3. Overview of the saddle-point method 55]
III.4. I hree combinatorial examples 55g
v III s Admissibihlv 5^4
vili. 6. Integer partitions ^74
Vili. 7. Saddle-points and linear differential equations. . 181
VIII. 8. Large powers 585
VIII. 9. Saddle-points and probability distributions 594
VIII. 10. Multiple saddle-points 600
VIII. 1 1. Perspecthe 606
Part C. RANDOM STRUCTURES 609
IX. MlLTIVARIATE ASYMPTOTICS ND LIMIT LAWS 6] 1
IX. 1. Limit laws and combinatorial structures 613
IX. 2. Discrete limit laws 620
IX. 3. Combinatorial instances of discrete laws 628
IX. 4. Continuous limit law s 638
IX. 5. Quasi-powers and Gaussian limit laws 644
IX. 6. Perturbation of meromorphic asymptotics 650
IX. 7. Perturbation of singularity analy sis asymptotics 666
IX. 8. Perturbation oí saddle-point asymptotic* 690
IX. 9. Local limit laws 694
IX. 10. Large deviations 699
IX. 11. Non-Gaussian continuous limits 703
IX. 12. Multivaiiate limit laws 715
IX. 13. Perspective 716
PartD. APPENDICES 719
Appendix A. Auxiliary Ei.f.mlntary Notions 721
A.I. Arithmetical functions 721
722
727
729
730
S 9
Î9
741
743
748
762
76~
Appendix C. CoNrf.PIsni Pi« is mi I ! Thi-ory 769
C.I. Probability spaces and measure 769
C.2. Random ariahles 771
C.3. Transforms ol distributions 772
A.2. Asymptotic notations
A.3. Combinatorial probabil itv
A.4. C cle construction
A.5. Formal power series
A.6. Lagrange inversion
A.7. Regular languages
A. 8. Stirling numbers.
A.9. Tree concepts
Appendix B. B sic Complex Anal1! sis
B.l. Algebraic elimination
B.2. Equi aleni definitions of analy licity
B.3. Gamma function
B.4. Holonoinic funclions
B.5. Implicit Function Theorem
B.6. Laplace s method
B.~. Niellili transforms
B.S. Sexeral complex ariabies
1.4 Special diMrihulioMN
( .5. Convergence in lau
liuti liKiK i in
Indi
sin
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| any_adam_object | 1 |
| author | Flajolet, Philippe Sedgewick, Robert 1946- |
| author_GND | (DE-588)112418317 |
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| classification_tum | MAT 602f MAT 050f |
| ctrlnum | (OCoLC)244767782 (DE-599)HBZHT015681142 |
| 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 |
| edition | 1. publ. |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T21:29:48Z |
| institution | BVB |
| isbn | 9780521898065 0521898064 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017063871 |
| oclc_num | 244767782 |
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| physical | XIII, 810 S. zahlr. graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| spelling | Flajolet, Philippe Verfasser aut Analytic combinatorics Philippe Flajolet & Robert Sedgewick 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2009 XIII, 810 S. zahlr. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke Combinatieleer gtt Combinatorial analysis Kombinatorische Analysis (DE-588)4164746-4 gnd rswk-swf Kombinatorische Analysis (DE-588)4164746-4 s DE-604 Sedgewick, Robert 1946- Verfasser (DE-588)112418317 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017063871&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Flajolet, Philippe Sedgewick, Robert 1946- Analytic combinatorics Combinatieleer gtt Combinatorial analysis Kombinatorische Analysis (DE-588)4164746-4 gnd |
| subject_GND | (DE-588)4164746-4 |
| title | Analytic combinatorics |
| title_auth | Analytic combinatorics |
| title_exact_search | Analytic combinatorics |
| title_full | Analytic combinatorics Philippe Flajolet & Robert Sedgewick |
| title_fullStr | Analytic combinatorics Philippe Flajolet & Robert Sedgewick |
| title_full_unstemmed | Analytic combinatorics Philippe Flajolet & Robert Sedgewick |
| title_short | Analytic combinatorics |
| title_sort | analytic combinatorics |
| topic | Combinatieleer gtt Combinatorial analysis Kombinatorische Analysis (DE-588)4164746-4 gnd |
| topic_facet | Combinatieleer Combinatorial analysis Kombinatorische Analysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017063871&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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