Frobenius partitions and the combinatorics of Ramanujan's \(_{1}\psi_{1}\) summation

DOI10.1006/jcta.2001.3205zbMath0998.11050OpenAlexW2049572756MaRDI QIDQ1604577

Sylvie Corteel, Jeremy Lovejoy

Publication date: 4 July 2002

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

Full work available at URL: https://doi.org/10.1006/jcta.2001.3205

zbMATH Keywords

Frobenius partitionsRamanujan's \(_1\psi_1\) summation

Mathematics Subject Classification ID

Combinatorial aspects of partitions of integers (05A17) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Elementary theory of partitions (11P81)

Related Items

The overpartition function modulo small powers of 2, Overpartition pairs, Partition bijections, a survey, Two families of buffered Frobenius representations of overpartitions, Particle seas and basic hypergeometric series., Combinatorial proofs of Ramanujan's \(_{1} \psi_{1}\) summation and the \(q\)-Gauss summation., Combinatorial proofs of identities in basic hypergeometric series, Overpartitions, lattice paths, and Rogers-Ramanujan identities, Overpartition pairs and two classes of basic hypergeometric series, Bilateral truncated Jacobi's identity, 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, Overpartitions, On Jackson’s proof of Ramanujan’s 1ψ1 summation formula

Cites Work

• A simple proof of Ramanujan's summation of the \(_1\Psi_1\)
• Generalized Frobenius partitions
• Chapter 16 of Ramanujan’s second notebook: theta-functions and 𝑞-series
• A Probabilistic Proof of Ramanujan’s ${}_1 \psi _1 $ Sum
• Shorter Notes: A Simple Proof of Ramanujan's 1 Ψ 1 Sum
• 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