Bijective proofs of basic hypergeometric series identities

DOI10.2140/pjm.1987.127.103zbMath0638.33002OpenAlexW2005330105WikidataQ114045267 ScholiaQ114045267MaRDI QIDQ1099307

J. T. Joichi, Dennis W. Stanton

Publication date: 1987

Published in: Pacific Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.pjm/1102699671

zbMATH Keywords

\(q\)-binomial theoremHeine's transformationWatson's transformation\(q\)-analogue of Gauss' theorem\(q\)-analogue of Rummer's theorem\(q\)-analogue of Saalschütz's theorembasic hypergeometric identityvery well poised evaluations

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 (17)

Interpretation of a basic hypergeometric identity with Lie characters and Young tableaux ⋮ On a theorem of Alladi and Gordon and the Gaussian polynomials ⋮ Bijections related to statistics on words ⋮ Combinatorics of the \(z^{AB}\) theorem ⋮ Parameter augmentation for basic hypergeometric series. II ⋮ Two families of buffered Frobenius representations of overpartitions ⋮ The number of equivalence classes arising from partition involutions ⋮ 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 ⋮ Un modèle symétrique pour l'identité de Al-Salam-Fields. (A symmetric model for the identity of Al-Salam-Fields) ⋮ Overpartition pairs and two classes of basic hypergeometric series ⋮ The Algorithm Z and Ramanujan's \({}_{1} \psi _{1}\) summation ⋮ Bijective matrix algebra ⋮ Ramanujan's lost notebook: combinatorial proofs of identities associated with Heine's transformation or partial theta functions ⋮ Overpartitions ⋮ The Gaussian coefficients and overpartitions

Cites Work

• Multiple series Rogers-Ramanujan type identities
• Binomial determinants, paths, and hook length formulae
• Identities in combinatorics. III: Further aspects of ordered set sorting
• A Rogers-Ramanujan bijection
• Bijective proofs of some classical partition identities
• On a calculus of partition functions
• Combinatorial problems of commutation and rearrangements
• A new property of partitions with applications to the Rogers-Ramanujan identities
• On the q-analog of Kummer's theorem and applications
• Generalized Frobenius partitions
• Method for constructing bijections for classical partition identities
• Chu's 1303 Identity Implies Bombieri's 1990 Norm-Inequality (Via an Identity of Beauzamy and Degot)
• Enumerative proofs of certain q-identities
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