The theory of partitions / George E. Andrews.
Discusses mathematics related to partitions of numbers into sums of positive integers.
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| Online Access: |
Full Text (via Cambridge) |
|---|---|
| Main Author: | |
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| Other title: | Cambridge books online. |
| Format: | eBook |
| Language: | English |
| Published: |
Cambridge :
Cambridge University Press,
1984.
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| Series: | Encyclopedia of mathematics and its applications ;
2. |
| Subjects: |
MARC
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| 100 | 1 | |a Andrews, George E., |d 1938- |1 https://id.oclc.org/worldcat/entity/E39PBJm96RJCb3xFv6qP6tB9Dq | |
| 245 | 1 | 4 | |a The theory of partitions / |c George E. Andrews. |
| 260 | |a Cambridge : |b Cambridge University Press, |c 1984. | ||
| 300 | |a 1 online resource (272 pages) | ||
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| 490 | 1 | |a Encyclopedia of mathematics and its applications ; |v 2 | |
| 520 | |a Discusses mathematics related to partitions of numbers into sums of positive integers. | ||
| 505 | 0 | |a Cover -- Half-title -- Title -- Copyright -- Dedication -- Contents -- Editor's Statement -- Preface to Paperback Edition -- Preface -- Chapter 1 The Elementary Theory of Partitions -- 1.1 Introduction -- 1.2 Infinite Product Generating Functions of One Variable -- 1.3 Graphical Representation of Partitions -- Examples -- Notes -- References -- Chapter 2 Infinite Series Generating Functions -- 2.1 Introduction -- 2.2 Elementary Series-Product Identities -- 2.3 Applications to Partitions -- Examples -- Notes -- References. | |
| 505 | 8 | |a Chapter 3 Restricted Partitions and Permutations -- 3.1 Introduction -- 3.2 The Generating Function for Restricted Partitions -- 3.3 Properties of Gaussian Polynomials -- 3.4 Permutations and Gaussian Multinomial Coefficients -- 3.5 The Unimodal Property -- Examples -- Notes -- References -- Chapter 4 Compositions and Simon Newcomb's Problem -- 4.1 Introduction -- 4.2 Composition of Numbers -- 4.3 Vector Compositions -- 4.4 Simon Newcomb's Problem -- Examples -- Notes -- References -- Chapter 5 The Hardy-Ramanujan-Rademacher Expansion of p(n) -- 5.1 Introduction. | |
| 505 | 8 | |a 5.2 The Formula for p(n) -- Examples -- Notes -- References -- Chapter 6 The Asymptotics of Infinite Product Generating Functions -- 6.1 Introduction -- 6.2 Proof of Theorem 6.2 -- 6.3 Applications of Theorem 6.2 -- Examples -- Notes -- References -- Chapter 7 Identities of the Rogers-Ramanujan Type -- 7.1 Introduction -- 7.2 The Generating Functions -- 7.3 The Rogers-Ramanujan Identities and Gordon's Generalization -- 7.4 The Gollnitz-Gordon Identities and Their Generalization -- Examples -- Notes -- References. | |
| 505 | 8 | |a Chapter 8 A General Theory of Partition Identities -- 8.1 Introduction -- 8.2 Foundations -- 8.3 Partition Ideals of Order 1 -- 8.4 Linked Partition Ideals -- Examples -- Notes -- References -- Chapter 9 Sieve Methods Related to Partitions -- 9.1 Introduction -- 9.2 Inclusion-Exclusion -- 9.3 A Sieve for Successive Ranks -- Examples -- Notes -- References -- Chapter 10 Congruence Properties of Partition Functions -- 10.1 Introduction -- 10.2 Rddseth's Theorem for Binary Partitions -- 10.3 Ramanujan's Conjecture for 5n -- Examples -- Notes -- References. | |
| 505 | 8 | |a Chapter 11 Higher-Dimensional Partitions -- 11.1 Introduction -- 11.2 Plane Partitions -- 11.3 The Knuth-Schensted Correspondence -- 11.4 Higher-Dimensional Partitions -- Examples -- Notes -- References -- Chapter 12 Vector or Multipartite Partitions -- 12.1 Introduction -- 12.2 Multipartite Generating Functions -- 12.3 Bell Polynomials and Formulas for Multipartite Partition Functions -- 12.4 Restricted Bipartite Partitions -- Examples -- Notes -- References -- Chapter 13 Partitions in Combinatorics -- 13.1 Introduction. | |
| 650 | 0 | |a Partitions (Mathematics) | |
| 650 | 0 | |a Number theory. | |
| 650 | 7 | |a Number theory |2 fast | |
| 650 | 7 | |a Partitions (Mathematics) |2 fast | |
| 710 | 2 | |a Cambridge University Press. | |
| 730 | 0 | |a Cambridge books online. | |
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| 830 | 0 | |a Encyclopedia of mathematics and its applications ; |v 2. | |
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