Integer Partitions

Provides a wide ranging introduction to partitions, accessible to any reader familiar with polynomials and infinite series.

George E. Andrews (Author), Kimmo Eriksson (Author)

9780521600903, Cambridge University Press

Paperback, published 11 October 2004

152 pages, 58 b/w illus. 5 tables 168 exercises
23 x 15.3 x 1 cm, 0.216 kg

'The clarity, accuracy, and motivation found in the writing should make the book especially attractive to students who want to begin to learn about the beautiful theory of partitions.' Combinatorics, Probability and Computing

The theory of integer partitions is a subject of enduring interest. A major research area in its own right, it has found numerous applications, and celebrated results such as the Rogers-Ramanujan identities make it a topic filled with the true romance of mathematics. The aim in this introductory textbook is to provide an accessible and wide ranging introduction to partitions, without requiring anything more of the reader than some familiarity with polynomials and infinite series. Many exercises are included, together with some solutions and helpful hints. The book has a short introduction followed by an initial chapter introducing Euler's famous theorem on partitions with odd parts and partitions with distinct parts. This is followed by chapters titled: Ferrers Graphs, The Rogers-Ramanujan Identities, Generating Functions, Formulas for Partition Functions, Gaussian Polynomials, Durfee Squares, Euler Refined, Plane Partitions, Growing Ferrers Boards, and Musings.

1. Introduction
2. Euler and beyond
3. Ferrers graphs
4. The Rogers-Ramanujan identities
5. Generating functions
6. Formulas for partition functions
7. Gaussian polynomials
8. Durfee squares
9. Euler refined
10. Plane partitions
11. Growing Ferrers boards
12. Musings
A. Infinite series and products
B. References
C. Solutions and hints.

Subject Areas: Number theory [PBH]