Integer partitions:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2004
|
| Ausgabe: | 1. publ. |
| Schlagworte: | |
| Online-Zugang: | Informationen des Verlegers Inhaltsverzeichnis Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | X, 141 S. graph. Darst. |
| ISBN: | 0521841186 0521600901 |
Internformat
MARC
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| 100 | 1 | |a Andrews, George E. |d 1938- |e Verfasser |0 (DE-588)122581342 |4 aut | |
| 245 | 1 | 0 | |a Integer partitions |c George E. Andrews ; Kimmo Eriksson |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2004 | |
| 300 | |a X, 141 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references and index | ||
| 650 | 7 | |a Partitie (wiskunde) |2 gtt | |
| 650 | 4 | |a Partitions (Mathématiques) | |
| 650 | 4 | |a aPartitions (Mathematics) | |
| 650 | 0 | 7 | |a Partition |g Zahlentheorie |0 (DE-588)4212684-8 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Partition |g Zahlentheorie |0 (DE-588)4212684-8 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Eriksson, Kimmo |d 1967- |e Verfasser |0 (DE-588)139282203 |4 aut | |
| 856 | 4 | |u http://www.loc.gov/catdir/description/cam041/2003069732.html |3 Informationen des Verlegers | |
| 856 | 4 | |u http://www.loc.gov/catdir/toc/cam041/2003069732.html |3 Inhaltsverzeichnis | |
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Datensatz im Suchindex
| _version_ | 1804133015565107200 |
|---|---|
| adam_text | Contents
Preface ix
1 Introduction 1
2 Euler and beyond 5
2.1 Set terminology 5
2.2 Bijective proofs of partition identities 6
2.3 A bijection for Euler s identity 8
2.4 Euler pairs 10
3 Ferrers graphs 14
3.1 Ferrers graphs and Ferrers boards 15
3.2 Conjugate partitions 16
3.3 An upper bound on p(n) 19
3.4 Bressoud s beautiful bijection 23
3.5 Euler s pentagonal number theorem 24
4 The Rogers Ramanujan identities 29
4.1 A fundamental type of partition identity 29
4.2 Discovering the first Rogers Ramanujan identity 31
4.3 Alder s conjecture 33
4.4 Schur s theorem 35
4.5 Looking for a bijective proof of the first
Rogers Ramanujan identity 39
4.6 The impact of the Rogers Ramanujan identities 41
5 Generating functions 42
5.1 Generating functions as products 42
5.2 Euler s theorem 47
5.3 Two variable generating functions 48
5.4 Euler s pentagonal number theorem 49
v
vi Contents
5.5 Congruences for pin) 51
5.6 Rogers Ramanujan revisited 52
6 Formulas for partition functions 55
6.1 Formula for p(n, 1) and p(n, 2) 55
6.2 A formula for p(n, 3) 57
6.3 A formula for p(n, 4) 58
6.4 Linwoopfo)1/ = 1 61
7 Gaussian polynomials 64
7.1 Properties of the binomial numbers 64
7.2 Lattice paths and the ^ binomial numbers 67
7.3 The ^ binomial theorem and the ^ binomial series 69
7.4 Gaussian polynomial identities 71
7.5 Limiting values of Gaussian polynomials 74
8 Durfee squares 75
8.1 Durfee squares and generating functions 75
8.2 Frobenius symbols 78
8.3 Jacobi s triple product identity 79
8.4 The Rogers Ramanujan identities 81
8.5 Successive Durfee squares 85
9 Euler refined 88
9.1 Sylvester s refinement of Euler 88
9.2 Fine s refinement 90
9.3 Lecture hall partitions 92
10 Plane partitions 99
10.1 Ferrers graphs and rhombus tilings 99
10.2 MacMahon s formulas 101
10.3 The formula for nr(h, y,; q) 103
11 Growing Ferrers boards 106
11.1 Random partitions 106
11.2 Posets of partitions 107
11.3 The hook length formula 110
11.4 Randomly growing Ferrers boards 113
11.5 Domino tilings 115
11.6 The arctic circle theorem 116
12 Musings 121
12.1 What have we left out? 121
12.2 Where can you go to undertake new explorations? 123
12.3 Where can one study the history of partitions? 124
12.4 Are there any unsolved problems left? 125
Contents vii
A On the convergence of infinite series and products 126
B References 129
C Solutions and hints to selected exercises 132
Index 139
|
| any_adam_object | 1 |
| author | Andrews, George E. 1938- Eriksson, Kimmo 1967- |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV019643033 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T20:02:00Z |
| institution | BVB |
| isbn | 0521841186 0521600901 |
| language | English |
| lccn | 2003069732 |
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| physical | X, 141 S. graph. Darst. |
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| spelling | Andrews, George E. 1938- Verfasser (DE-588)122581342 aut Integer partitions George E. Andrews ; Kimmo Eriksson 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2004 X, 141 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Partitie (wiskunde) gtt Partitions (Mathématiques) aPartitions (Mathematics) Partition Zahlentheorie (DE-588)4212684-8 gnd rswk-swf Partition Zahlentheorie (DE-588)4212684-8 s DE-604 Eriksson, Kimmo 1967- Verfasser (DE-588)139282203 aut http://www.loc.gov/catdir/description/cam041/2003069732.html Informationen des Verlegers http://www.loc.gov/catdir/toc/cam041/2003069732.html Inhaltsverzeichnis HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012971866&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Andrews, George E. 1938- Eriksson, Kimmo 1967- Integer partitions Partitie (wiskunde) gtt Partitions (Mathématiques) aPartitions (Mathematics) Partition Zahlentheorie (DE-588)4212684-8 gnd |
| subject_GND | (DE-588)4212684-8 |
| title | Integer partitions |
| title_auth | Integer partitions |
| title_exact_search | Integer partitions |
| title_full | Integer partitions George E. Andrews ; Kimmo Eriksson |
| title_fullStr | Integer partitions George E. Andrews ; Kimmo Eriksson |
| title_full_unstemmed | Integer partitions George E. Andrews ; Kimmo Eriksson |
| title_short | Integer partitions |
| title_sort | integer partitions |
| topic | Partitie (wiskunde) gtt Partitions (Mathématiques) aPartitions (Mathematics) Partition Zahlentheorie (DE-588)4212684-8 gnd |
| topic_facet | Partitie (wiskunde) Partitions (Mathématiques) aPartitions (Mathematics) Partition Zahlentheorie |
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