The Theory of Partitions

Develops the theory of partitions, and considers the many theoretical aspects of this subject, which have in turn recently found applications to statistical mechanics, computer science and other branches of mathematics. Suitable for students as well as researchers in combinatorics, analysis and number theory.

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


Zusammenfassung
The partitions of a number are the ways of writing that number as sums of positive integers. For example, the five partitions of 4 are 4, 3+1, 2+2, 2+1+1, and 1+1+1+1. This book considers the many theoretical aspects of this subject, which have in turn recently found applications to statistical mechanics, computer science and other branches of mathematics.

Inhalt
1. The elementary theory of partitions; 2. Infinite series generating functions; 3. Restricted partitions and permutations; 4. Compositions and Simon Newcomb's problem; 5. The Hardy-Ramanujan-Rademacher expansion of p(n); 6. The asymptotics of infinite product generating functions; 7. Identities of the Rogers-Ramanujan type; 8. A general theory of partition identities; 9. Sieve methods related to partitions; 10. Congruence properties of partition functions; 11. Higher-dimensional partitions; 12. Vector or multipartite partitions; 13. Partitions in combinatorics; 14. Computations for partitions.

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