Lectures on generating functions:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch Russisch |
| Veröffentlicht: |
Providence, RI
American Math. Soc.
2003
|
| Schriftenreihe: | Student mathematical library
23 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013359876&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Aus dem Russ. übers. |
| Umfang: | XV, 148 S. Ill., graph. Darst. 22 cm |
| ISBN: | 9780821834817 |
Internformat
MARC
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| 100 | 1 | |a Lando, Sergej K. |d 1955- |e Verfasser |0 (DE-588)128627158 |4 aut | |
| 240 | 1 | 0 | |a Lekcii o proizvodjaščich funkcijach |
| 245 | 1 | 0 | |a Lectures on generating functions |c S. K. Lando |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 2003 | |
| 300 | |a XV, 148 S. |b Ill., graph. Darst. |c 22 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Student mathematical library |v 23 | |
| 500 | |a Aus dem Russ. übers. | ||
| 650 | 7 | |a Combinatória |2 larpcal | |
| 650 | 4 | |a Fonctions génératrices | |
| 650 | 4 | |a aGenerating functions | |
| 650 | 0 | 7 | |a Kombinatorik |0 (DE-588)4031824-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Erzeugende Funktion |0 (DE-588)4152979-0 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Erzeugende Funktion |0 (DE-588)4152979-0 |D s |
| 689 | 0 | 1 | |a Kombinatorik |0 (DE-588)4031824-2 |D s |
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| 830 | 0 | |a Student mathematical library |v 23 |w (DE-604)BV013184751 |9 23 | |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-013359876 | |
Datensatz im Suchindex
| DE-BY-TUM_call_number | 0049 MAT 050f 2009 A 9667 |
|---|---|
| DE-BY-TUM_katkey | 1710316 |
| DE-BY-TUM_location | LSB |
| DE-BY-TUM_media_number | 040020764490 |
| _version_ | 1821935449340379138 |
| adam_text | Contents
Preface to the English Edition xi
Preface xiii
Chapter 1. Formal Power Series and Generating Functions.
Operations with Formal Power Series. Elementary
Generating Functions 1
§1 1. The lucky tickets problem 1
§1.2. First conclusions 6
§1.3. Generating functions and operations with them 7
§1.4. Elementary generating functions 10
§1.5. Differentiating and integrating generating functions 12
§1.6. The algebra and the topology of formal power series 13
§1.7. Problems 14
Chapter 2. Generating Functions for Well known Sequences 17
§2.1. Geometric series 17
§2.2. The Fibonacci sequence 18
§2.3. Recurrence relations and rational generating functions 21
§2.4. The Hadamard product of generating functions 23
§2.5. Catalan numbers 25
vii
viii Contents
§2.6. Problems 30
Chapter 3. Unambiguous Formal Grammars. The Lagrange
Theorem 35
§3.1. The Dyck Language 35
§3.2. Productions in the Dyck language 36
§3.3. Unambiguous formal grammars 38
§3.4. The Lagrange equation and the Lagrange theorem 42
§3.5. Problems 43
Chapter 4. Analytic Properties of Functions Represented
as Power Series and the Asymptotics of their
Coefficients 47
§4.1. Exponential estimates for asymptotics 47
§4.2. Asymptotics of hypergeometric sequences 50
§4.3. Asymptotics of coefficients of functions related by the
Lagrange equation 54
§4.4. Asymptotics of coefficients of generating series and
singularities on the boundary of the disc of convergence 56
§4.5. Problems 58
Chapter 5. Generating Functions of Several Variables 59
§5.1. The Pascal triangle 59
§5.2. Exponential generating functions 61
§5.3. The Dyck triangle 63
§5.4. The Bernoulli Euler triangle and enumeration of snakes 64
§5.5. Representing generating functions as continued
fractions 72
§5.6. The Euler numbers in the triangle with multiplicities 78
§5.7. Congruences in integer sequences 79
§5.8. How to solve ordinary differential equations in
generating functions 82
§5.9. Problems 83
Chapter 6. Partitions and Decompositions 87
Contents ix
§6.1. Partitions and decompositions 87
§6.2. The Euler identity 92
§6.3. Set partitions and continued fractions 95
§6.4. Problems 98
Chapter 7. Dirichlet Generating Functions and the Inclusion
Exclusion Principle 101
§7.1. The inclusion exclusion principle 101
§7.2. Dirichlet generating functions and operations with
them 104
§7.3. Mobius inversion 107
§7.4. Multiplicative sequences 109
§7.5. Problems 110
Chapter 8. Enumeration of Embedded Graphs 113
§8.1. Enumeration of marked trees 113
§8.2. Generating functions for non marked, marked,
ordered, and cyclically ordered objects 119
§8.3. Enumeration of plane and binary trees 120
§8.4. Graph embeddings into surfaces 122
§8.5. On the number of gluings of a polygon 132
§8.6. Proof of the Harer Zagier theorem 136
§8.7. Problems 140
Final and Bibliographical Remarks 143
Bibliography 145
Index 147
|
| any_adam_object | 1 |
| author | Lando, Sergej K. 1955- |
| author_GND | (DE-588)128627158 |
| author_facet | Lando, Sergej K. 1955- |
| author_role | aut |
| author_sort | Lando, Sergej K. 1955- |
| author_variant | s k l sk skl |
| building | Verbundindex |
| bvnumber | BV020038772 |
| callnumber-first | Q - Science |
| callnumber-label | QA164 |
| callnumber-raw | QA164.8 |
| callnumber-search | QA164.8 |
| callnumber-sort | QA 3164.8 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 170 SK 420 |
| classification_tum | MAT 339f MAT 050f |
| ctrlnum | (OCoLC)53021578 (DE-599)BVBBV020038772 |
| 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 16 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV020038772 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T12:10:45Z |
| institution | BVB |
| isbn | 9780821834817 |
| language | English Russian |
| lccn | 2003055939 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-013359876 |
| oclc_num | 53021578 |
| open_access_boolean | |
| owner | DE-824 DE-703 DE-83 DE-91G DE-BY-TUM |
| owner_facet | DE-824 DE-703 DE-83 DE-91G DE-BY-TUM |
| physical | XV, 148 S. Ill., graph. Darst. 22 cm |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | Student mathematical library |
| series2 | Student mathematical library |
| spellingShingle | Lando, Sergej K. 1955- Lectures on generating functions Student mathematical library Combinatória larpcal Fonctions génératrices aGenerating functions Kombinatorik (DE-588)4031824-2 gnd Erzeugende Funktion (DE-588)4152979-0 gnd |
| subject_GND | (DE-588)4031824-2 (DE-588)4152979-0 |
| title | Lectures on generating functions |
| title_alt | Lekcii o proizvodjaščich funkcijach |
| title_auth | Lectures on generating functions |
| title_exact_search | Lectures on generating functions |
| title_full | Lectures on generating functions S. K. Lando |
| title_fullStr | Lectures on generating functions S. K. Lando |
| title_full_unstemmed | Lectures on generating functions S. K. Lando |
| title_short | Lectures on generating functions |
| title_sort | lectures on generating functions |
| topic | Combinatória larpcal Fonctions génératrices aGenerating functions Kombinatorik (DE-588)4031824-2 gnd Erzeugende Funktion (DE-588)4152979-0 gnd |
| topic_facet | Combinatória Fonctions génératrices aGenerating functions Kombinatorik Erzeugende Funktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013359876&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV013184751 |
| work_keys_str_mv | AT landosergejk lekciioproizvodjascichfunkcijach AT landosergejk lecturesongeneratingfunctions |
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