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The theory of partitions. (English) Zbl 0371.10001

Encyclopedia of Mathematics and Its Applications. Vol. 2. Section: Number Theory. Reading, Mass. etc.: Addison-Wesley Publishing Company, Advanced Book Program. xiv, 255 p. $ 16.50 (1976).
see the scanned pages
This book is very well written. despite the large amount of ground it is quite readable. It is an excellent introduction to a fascinating subject.

MSC:

11-02 Research exposition (monographs, survey articles) pertaining to number theory
11P81 Elementary theory of partitions
11P82 Analytic theory of partitions
11P83 Partitions; congruences and congruential restrictions
11P84 Partition identities; identities of Rogers-Ramanujan type
05-02 Research exposition (monographs, survey articles) pertaining to combinatorics
05A15 Exact enumeration problems, generating functions
05A17 Combinatorial aspects of partitions of integers
05A19 Combinatorial identities, bijective combinatorics

Digital Library of Mathematical Functions:

§17.18 Methods of Computation ‣ Computation ‣ Chapter 17 q -Hypergeometric and Related Functions
§17.2(iii) Binomial Theorem ‣ §17.2 Calculus ‣ Properties ‣ Chapter 17 q -Hypergeometric and Related Functions
§17.2(vi) Rogers–Ramanujan Identities ‣ §17.2 Calculus ‣ Properties ‣ Chapter 17 q -Hypergeometric and Related Functions
§17.5 ϕ 0 0 , ϕ 0 1 , ϕ 1 1 Functions ‣ Properties ‣ Chapter 17 q -Hypergeometric and Related Functions
Chapter 17 q -Hypergeometric and Related Functions
§26.10(iii) Recurrence Relations ‣ §26.10 Integer Partitions: Other Restrictions ‣ Properties ‣ Chapter 26 Combinatorial Analysis
§26.10(ii) Generating Functions ‣ §26.10 Integer Partitions: Other Restrictions ‣ Properties ‣ Chapter 26 Combinatorial Analysis
§26.10(iv) Identities ‣ §26.10 Integer Partitions: Other Restrictions ‣ Properties ‣ Chapter 26 Combinatorial Analysis
§26.10(vi) Bessel-Function Expansion ‣ §26.10 Integer Partitions: Other Restrictions ‣ Properties ‣ Chapter 26 Combinatorial Analysis
§26.10(v) Limiting Form ‣ §26.10 Integer Partitions: Other Restrictions ‣ Properties ‣ Chapter 26 Combinatorial Analysis
§26.11 Integer Partitions: Compositions ‣ Properties ‣ Chapter 26 Combinatorial Analysis
§26.12(iv) Limiting Form ‣ §26.12 Plane Partitions ‣ Properties ‣ Chapter 26 Combinatorial Analysis
§26.14(ii) Generating Functions ‣ §26.14 Permutations: Order Notation ‣ Properties ‣ Chapter 26 Combinatorial Analysis
§26.14(i) Definitions ‣ §26.14 Permutations: Order Notation ‣ Properties ‣ Chapter 26 Combinatorial Analysis
§26.16 Multiset Permutations ‣ Properties ‣ Chapter 26 Combinatorial Analysis
§26.16 Multiset Permutations ‣ Properties ‣ Chapter 26 Combinatorial Analysis
§26.21 Tables ‣ Computation ‣ Chapter 26 Combinatorial Analysis
§26.9(ii) Generating Functions ‣ §26.9 Integer Partitions: Restricted Number and Part Size ‣ Properties ‣ Chapter 26 Combinatorial Analysis
§26.9(i) Definitions ‣ §26.9 Integer Partitions: Restricted Number and Part Size ‣ Properties ‣ Chapter 26 Combinatorial Analysis
§26.9(i) Definitions ‣ §26.9 Integer Partitions: Restricted Number and Part Size ‣ Properties ‣ Chapter 26 Combinatorial Analysis
§26.9(iv) Limiting Form ‣ §26.9 Integer Partitions: Restricted Number and Part Size ‣ Properties ‣ Chapter 26 Combinatorial Analysis
§27.14(vi) Ramanujan’s Tau Function ‣ §27.14 Unrestricted Partitions ‣ Additive Number Theory ‣ Chapter 27 Functions of Number Theory
Chapter 27 Functions of Number Theory