Combinatorial proofs of Ramanujan's \(_{1} \psi_{1}\) summation and the \(q\)-Gauss summation.

DOI10.1016/j.jcta.2003.10.002zbMath1048.11078OpenAlexW1977667882MaRDI QIDQ1427009

Ae Ja Yee

Publication date: 14 March 2004

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcta.2003.10.002

zbMATH Keywords

\(F\)-partitionsFrobenius partition

Mathematics Subject Classification ID

Partitions; congruences and congruential restrictions (11P83) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Elementary theory of partitions (11P81) Analytic theory of partitions (11P82)

Related Items (17)

A reciprocity theorem for certain \(q\)-series found in Ramanujan's lost notebook ⋮ Overpartition pairs ⋮ Some new \(q\)-series identities through an extended Bailey transform ⋮ Two \(q\)-operational equations and Hahn polynomials ⋮ Combinatorial proofs of identities in basic hypergeometric series ⋮ Overpartitions, lattice paths, and Rogers-Ramanujan identities ⋮ Overpartition pairs and two classes of basic hypergeometric series ⋮ An overpartition analogue of the \(q\)-binomial coefficients ⋮ Overpartition pairs modulo powers of 2 ⋮ The Algorithm Z and Ramanujan's \({}_{1} \psi _{1}\) summation ⋮ A short proof of Ramanujan's famous \(_1\psi_1\) summation formula ⋮ Ramanujan's lost notebook: combinatorial proofs of identities associated with Heine's transformation or partial theta functions ⋮ RANK AND CONGRUENCES FOR OVERPARTITION PAIRS ⋮ Limit Shapes via Bijections ⋮ A short note on the overpartition function ⋮ On Jackson’s proof of Ramanujan’s 1ψ1 summation formula ⋮ The Gaussian coefficients and overpartitions

Cites Work

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• Partition bijections, a survey
• Bijective proofs of basic hypergeometric series identities
• Particle seas and basic hypergeometric series.
• Frobenius partitions and the combinatorics of Ramanujan's \(_{1}\psi_{1}\) summation
• Combinatorial proofs of generating function identities for F-partitions
• Generalized Frobenius partitions
• Chapter 16 of Ramanujan’s second notebook: theta-functions and 𝑞-series
• A Proof of Ramanujan’s Identity by Use of Loop Integrals
• Ramanujan's Extensions of the Gamma and Beta Functions
• Shorter Notes: A Simple Proof of Ramanujan's 1 Ψ 1 Sum
• Overpartitions
• An Enumerative Proof of An Identity of Jacobi
• Shorter Notes: On Ramanujan's Summation of 1 ψ 1 (a; b; z)
• On a Transformation of Bilateral Series with Applications
• Beiträge zur Theorie der Heineschen Reihen. Die 24 Integrale der hypergeometrischen q‐Differenzengleichung. Das q‐Analogon der Laplace‐Transformation
• On Lerch's Transcendant and the Basic Bilateral Hypergeometric Series ₂ ψ₂
• ON THE BASIC BILATERAL HYPERGEOMETRIC SERIES ₂ψ₂

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