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Integer partitions:

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Main Authors:	Andrews, George E. 1938- (Author), Eriksson, Kimmo 1967- (Author)
Format:	Book
Language:	English
Published:	Cambridge [u.a.] Cambridge Univ. Press 2004
Edition:	1. publ.
Subjects:	Partitie (wiskunde) Partitions (Mathématiques) aPartitions (Mathematics) Partition > Zahlentheorie
Online Access:	Informationen des Verlegers Inhaltsverzeichnis Inhaltsverzeichnis
Item Description:	Includes bibliographical references and index
Physical Description:	X, 141 S. graph. Darst.
ISBN:	0521841186 0521600901

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MARC


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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-search	512.7/3
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discipline	Mathematik
edition	1. publ.
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isbn	0521841186 0521600901
language	English
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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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