This book develops the theory of partitions. Simply put, the partitions of a number are the ways of writing that number as sums of positive integers. For example, the five partitions of 4 are 4, 3+1, 2+2, 2+1+1, and 1+1+1+1. Surprisingly, such a simple matter requires some deep mathematics for its study. This book considers the many theoretical aspects of this subject, which have in turn recently found applications to statistical mechanics, computer science and other branches of mathematics. With minimal prerequisites, this book is suitable for students as well as researchers in combinatorics, analysis, and number theory.
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'A good introduction to a fascinating subject ... a very pleasant book to read.' Richard Askley, Bulletin of the AMS
'There is no doubt that this book will continue to serve as a basic and indispensable source of information for everyone interested in this fascinating subject.' European Mathematical Society
'There is no doubt that this book will continue to serve as a basic and indispensable source of information for everyone interested in this fascinating subject.' European Mathematical Society
Book Description
The partitions of a number are the ways of writing that number as sums of positive integers. For example, the five partitions of 4 are 4, 3+1, 2+2, 2+1+1, and 1+1+1+1. This book considers the many theoretical aspects of this subject, which have in turn recently found applications to statistical mechanics, computer science and other branches of mathematics.
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29 of 29 people found the following review helpful:
5.0 out of 5 stars
Basic reference on partitions and q-series,
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This review is from: The Theory of Partitions (Encyclopedia of Mathematics and its Applications) (Paperback)
This is *the* classic and most essential reference on the theory of partitions and related q-series written by the leading authority on the subject. It requires almost no technical prerequisites, starts from scratch, and proceeds in a very clear and orderly manner towards some of the more elaborate aspects of the subject. If you (plan to) work on this subject, buy it.The book was written in 1976, and as such does not cover the more recent developments, though the bibliography has been updated (to a limited degree) for the current 1998 paperback edition. However, after all these years, it remains *the* introduction to the subject (with the possible exception of chapter 14 on computational methods, which is definitely outdated), and can be supplemented only by Gaspar and Rahman's 'Basic Hypergeometric Series'. I taught a higher undergraduate level course based on chapters 1, 2, 3, 7 and 9, and my students definitely found these chapters to be highly readable. My one and only complaint is to Cambridge University Press: Dover has shown that paperbacks can be produced in such a way that they can be opened completely flat without being damaged, and quite cheaply too. Why can't you adopt the same technology?
5.0 out of 5 stars
A real classic,
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This review is from: The Theory of Partitions (Encyclopedia of Mathematics and its Applications) (Paperback)
The Theory of Partitions is the classic reference book for the basics of partitions.
The first chapter is low-level, and then it goes upwards. Also, some applications are included.
8 of 19 people found the following review helpful:
5.0 out of 5 stars
A Classic,
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This review is from: The Theory of Partitions (Encyclopedia of Mathematics and its Applications) (Paperback)
This is the bible for the theory of partitions
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Inside This Book
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First Sentence:
In this book we shall study in depth the fundamental additive decomposition process: the representation of positive integers by sums of other positive integers. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
multipartite numbers, multipartite partitions, partition ideals, statistical group theory, pentagonal number theorem, topological sequences, plane partitions, partition identities, ordinary partition, combinatory analysis, strict decrease, triple product identity, finite vector spaces, basic hypergeometric series, partition theorem, parts congruent, binary partitions, empty partition, congruence properties, successive ranks, greater index, type enumerated, combinatorial interpretations, combinatorial proof Key Phrases - Capitalized Phrases (CAPs): (learn more)
New York, Cambridge Univ, London Math, Duke Math, Simon Newcomb, Addison-Wesley Publishing Company, Advanced Book Program, Cambridge Phil, Its Applications, The Theory of Partitions Copyright, Oxford Ser, References Andrews, Academic Press, Gian-Carlo Rota, Discrete Math, Theory of Numbers, Acta Arith, The Elementary Theory of Partitions Chap, Acta Math, Aequationes Math, Glasgow Math, Lecture Notes, Messenger of Math, Sieve Methods Related, Congruence Properties of Partition Functions Chap New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
In this book we shall study in depth the fundamental additive decomposition process: the representation of positive integers by sums of other positive integers. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
multipartite numbers, multipartite partitions, partition ideals, statistical group theory, pentagonal number theorem, topological sequences, plane partitions, partition identities, ordinary partition, combinatory analysis, strict decrease, triple product identity, finite vector spaces, basic hypergeometric series, partition theorem, parts congruent, binary partitions, empty partition, congruence properties, successive ranks, greater index, type enumerated, combinatorial interpretations, combinatorial proof Key Phrases - Capitalized Phrases (CAPs): (learn more)
New York, Cambridge Univ, London Math, Duke Math, Simon Newcomb, Addison-Wesley Publishing Company, Advanced Book Program, Cambridge Phil, Its Applications, The Theory of Partitions Copyright, Oxford Ser, References Andrews, Academic Press, Gian-Carlo Rota, Discrete Math, Theory of Numbers, Acta Arith, The Elementary Theory of Partitions Chap, Acta Math, Aequationes Math, Glasgow Math, Lecture Notes, Messenger of Math, Sieve Methods Related, Congruence Properties of Partition Functions Chap New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 23
books:
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100
books
cite this book:
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- Combinatory Analysis (Dover Books on Mathematics) by Percy A. MacMahon on 11 pages
- Number Theory (Dover Books on Mathematics) by George E. Andrews on 10 pages
- Modular Functions in Analytic Number Theory: Second Edition by Marvin I. Knopp on 4 pages
- An Introduction to the Theory of Numbers (Oxford Science Publications) by G. H. Hardy in Front Matter, page 15, and page 32
- Special Functions (Encyclopedia of Mathematics and its Applications) by George E. Andrews on page 52, page 119, and page 138
See all 23 books this book cites
- Ramanujan: Essays and Surveys (History of Mathematics, V. 22) by Bruce C. Berndt on 4 pages
- Special Functions 2000: Current Perspectives and Future Dire (NATO Science Series II: Mathematics, Physics and Chemistry) by Joaquin Bustoz on page 21, page 218, and page 252
- Physical Combinatorics (Progress in Mathematics) by Masaki Kashiwara on page 102, page 182, and page 215
- Number Theory and Discrete Mathematics (Trends in Mathematics) by A.K. Agarwal on page 46, page 289, and Back Matter
- Symbolic Computation, Number Theory, Special Functions, Physics and Combinatorics (Developments in Mathematics) by Frank G. Garvan on page 57, page 132, and page 265
See all 100 books citing this book
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