Combinatorial proofs of identities in Ramanujan's lost notebook associated with the Rogers-Fine identity and false theta functions

DOI10.1007/s00026-003-0194-yzbMath1037.05005OpenAlexW2144589933MaRDI QIDQ1424253

Ae Ja Yee, Bruce C. Berndt

Publication date: 11 March 2004

Published in: Annals of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00026-003-0194-y

zbMATH Keywords

partitions of integersFerrers graphsFranklin's involutionMacMahon's \(k\)-modular partitions

Mathematics Subject Classification ID

Combinatorial identities, bijective combinatorics (05A19) Combinatorial aspects of partitions of integers (05A17) Elementary theory of partitions (11P81)

Related Items (13)

Partial theta functions and mock modular forms as \(q\)-hypergeometric series ⋮ Some new \(q\)-series identities through an extended Bailey transform ⋮ Asymptotics and sign patterns for coefficients in expansions of Habiro elements ⋮ Identities on mex-related partitions ⋮ Asymptotic behavior of partial and false theta functions arising from Jacobi forms and regularized characters ⋮ The minimal excludant and Schmidt's partition theorem ⋮ Partitions with fixed largest hook length ⋮ BILATERAL BAILEY LEMMA AND FALSE THETA FUNCTIONS ⋮ Ramanujan's lost notebook: combinatorial proofs of identities associated with Heine's transformation or partial theta functions ⋮ Combinatorial proofs for identities related to generalizations of the mock theta functions \(\omega (q)\) and \(\nu (q)\) ⋮ Mock and mixed mock modular forms in the lower half-plane ⋮ A bijective proof of a false theta function identity from Ramanujan's lost notebook ⋮ Combinatorial proof of a partial theta function identity of Warnaar

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