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The theory of partitions / George E. Andrews.

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

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Bibliographic Details
Online Access: Full Text (via Cambridge)
Main Author: Andrews, George E., 1938-
Corporate Author: Cambridge University Press
Other title:Cambridge books online.
Format: eBook
Language:English
Published: Cambridge : Cambridge University Press, 1984.
Series:Encyclopedia of mathematics and its applications ; 2.
Subjects:
Partitions (Mathematics)
Number theory.
Number theory
Table of Contents:
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.

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