Andrews, George E. 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. Reviewer: Leonard Carlitz (Durham, N.C.) Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 18 ReviewsCited in 825 Documents 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 PDF BibTeX XML 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 ₀ϕ₀,₁ϕ₀,₁ϕ₁ 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 Online Encyclopedia of Integer Sequences: Number of monomial ideals in two variables that are artinian, integrally closed and of colength n. Number of monomial ideals in two variables x, y that are Artinian, integrally closed, of colength n and contain x^2. Number of monomial ideals in two variables x, y that are Artinian, integrally closed, of colength n and contain x^3. Number of monomial ideals in two variables x, y that are Artinian, integrally closed, of colength n and contain x^4.