The theory of partitions
著者
書誌事項
The theory of partitions
（Encyclopedia of mathematics and its applications / edited by G.-C. Rota, v. 2 . Section,
Cambridge University Press, 1984
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注記
Imprint and ISBN from label on t.p. verso. Imprint on t.p.: Reading, Mass. : Addison-Wesley Pub. Co., Advanced Book Program, 1976
Publication taken over by Cambridge University Press in 1984 with a new copyright date
Includes bibliographies and indexes
内容説明・目次
内容説明
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.
目次
- 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.
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