A NEW COMBINATORIAL STUDY OF THE ROGERS–FINE IDENTITY AND A RELATED PARTIAL THETA SERIES

DOI10.1142/S1793042109002675zbMath1180.05013MaRDI QIDQ3652600

Krishnaswami Alladi

Publication date: 15 December 2009

Published in: International Journal of Number Theory (Search for Journal in Brave)

zbMATH Keywords

partitionssliding operationRogers-Fine identitypartial theta seriesDurfee squaresCauchy's identityRogers-Fine variant

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Combinatorial identities, bijective combinatorics (05A19) Combinatorial aspects of partitions of integers (05A17) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Elementary theory of partitions (11P81)

Related Items (8)

Variants of classical \(q\)-hypergeometric identities and partition implications ⋮ Partitions with Non-Repeating Odd Parts and Q-Hypergeometric Identities ⋮ Asymptotic behavior of partial and false theta functions arising from Jacobi forms and regularized characters ⋮ Universal mock theta functions and two-variable Hecke-Rogers identities ⋮ An overpartition analogue of \(q\)-binomial coefficients. II: Combinatorial proofs and \((q,t)\)-log concavity ⋮ Euler’s Partition Theorem and Refinements Without Appeal to Infinite Products ⋮ A framework for modular properties of false theta functions ⋮ A bijective proof of a limiting case of Watson's \(_8\phi_7\) transformation formula

Cites Work

• The \(q\)-variations of Sylvester's bijection between odd and strict partitions
• Two theorems of Gauss and allied identities proved arithmetically
• A combinatorial correspondence related to Göllnitz’ (big) partition theorem and applications
• Partition identities involving gaps and weights

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