Integer Partitions

ISBN-13: 9780521600903 / Angielski / Miękka / 2004 / 152 str.

George E. Andrews; Kimmo Eriksson

Opis

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.

Recenzje

'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

Spis treści

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.