Integer partitions
著者
書誌事項
Integer partitions
Cambridge University Press, 2004
- : hardback
- : pbk
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注記
Includes bibliographical references (p. 129-131) and index
内容説明・目次
内容説明
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.
目次
- 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.
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