Integer Partitions [Paperback]

Provides a wide ranging introduction to partitions, accessible to any reader familiar with polynomials and infinite series.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 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 theory of integer partitions is a subject of enduring interest as well as a major research area. It has found numerous applications, including celebrated results such as the Rogers-Ramanujan identities. The aim of this introductory textbook is to provide an accessible and wide-ranging introduction to partitions, without requiring anything more than some familiarity with polynomials and infinite series. Many exercises are included, together with some solutions and helpful hints.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. lóZ