A general theory of identities of the Rogers-Ramanujan type

DOI10.1090/S0002-9904-1974-13616-5zbMath0301.10016OpenAlexW2109930638MaRDI QIDQ4056078

George E. Andrews

Publication date: 1974

Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9904-1974-13616-5

zbMATH Keywords

unsolved problemsRogers-Ramanujan identitiespartition identitieslinked partition idealssurvey of recent workfinite linear q-difference equations with polynomial coefficientssieves in theory of partitionssolutions represented by higher dimensional q-series

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Combinatorial identities, bijective combinatorics (05A19) Combinatorial aspects of partitions of integers (05A17) Research exposition (monographs, survey articles) pertaining to number theory (11-02) Elementary theory of partitions (11P81) Classical hypergeometric functions, ({}_2F_1) (33C05) Partition identities; identities of Rogers-Ramanujan type (11P84)

Related Items (17)

Linked partition ideals and the Alladi-Schur theorem ⋮ Linked partition ideals and kanade-Russell conjectures ⋮ Fast computation of the \(N\)-th term of a \(q\)-holonomic sequence and applications ⋮ Linked partition ideals and Andrews-Gordon type series for Alladi and Gordon's extension of Schur's identity ⋮ Linked partition ideals and Euclidean billiard partitions ⋮ Bijections, generalizations, and other properties of sequentially congruent partitions ⋮ Linked partition ideals, directed graphs and \(q\)-multi-summations ⋮ Linked partition ideals and a family of quadruple summations ⋮ Unnamed Item ⋮ Linked partition ideals and a Schur-type identity of Andrews ⋮ Certain transformation formulae for polybasic hypergeometric series ⋮ Products of vector valued Eisenstein series ⋮ Classical partition functions and the \(U(n+1)\) Rogers-Selberg identity ⋮ Lie algebraic approaches to classical partition identities ⋮ Bilateral Bailey lemma and Rogers-Ramanujan identities ⋮ Linear differential equations as a data structure ⋮ CERTAIN NEW WP-BAILEY PAIRS AND BASIC HYPERGEOMETRIC SERIES IDENTITIES

Cites Work

• Some continued fractions of the Rogers-Ramanujan type
• Partition identities
• Generalizations of the Rogers-Ramanujan identities
• On the general Rogers-Ramanujan theorem
• On the Alder Polynomials and a New Generalization of the Rogers-Ramanujan Identities
• Partition Theorems Related to Some Identities of Rogers and Watson
• Linear 𝑞-difference equations
• ON q-DIFFERENCE EQUATIONS FOR CERTAIN WELL-POISED BASIC HYPERGEOMETRIC SERIES
• A new generalization of Schur's second partition theorem
• A General Theorem on Partitions with Difference Conditions
• A Generalization of the Classical Partition Theorems
• Summations and Transformations for Basic Appell Series
• Sieves in the Theory of Partitions
• Identities of the Rogers-Ramanujan Type
• Beiträge zur Theorie der Heineschen Reihen. Die 24 Integrale der hypergeometrischen q‐Differenzengleichung. Das q‐Analogon der Laplace‐Transformation
• Über die höheren Heineschen Reihen und eine einheitliche Theorie der sogenannten speziellen Funktionen
• Some Identities in Combinatory Analysis
• A New Proof of Rogers's Transformations of Infinite Series
• Further Identities of the Rogers-Ramanujan Type
• ON BASIC DOUBLE HYPERGEOMETRIC FUNCTIONS
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