The Theory of Partitions

Discusses mathematics related to partitions of numbers into sums of positive integers.

George E. Andrews (Author)

9780521637664, Cambridge University Press

Paperback, published 28 July 1998

272 pages, 12 b/w illus. 5 tables
23.1 x 15.2 x 1.8 cm, 0.4 kg

'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

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.

1. The elementary theory of partitions
2. Infinite series generating functions
3. Restricted partitions and permutations
4. Compositions and Simon Newcomb's problem
5. The Hardy-Ramanujan-Rademacher expansion of p(n)
6. The asymptotics of infinite product generating functions
7. Identities of the Rogers-Ramanujan type
8. A general theory of partition identities
9. Sieve methods related to partitions
10. Congruence properties of partition functions
11. Higher-dimensional partitions
12. Vector or multipartite partitions
13. Partitions in combinatorics
14. Computations for partitions.

Subject Areas: Number theory [PBH]