Exotic Bailey-Slater spt-functions. II: Hecke-Rogers-type double sums and Bailey pairs from groups A, C, E

DOI10.1016/j.aim.2016.05.021zbMath1348.11079arXiv1501.06843OpenAlexW2240490256MaRDI QIDQ2629114

Chris Jennings-Shaffer, Frank G. Garvan

Publication date: 20 July 2016

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1501.06843

zbMATH Keywords

partitionscongruencesnumber theoryBailey pairsBailey's lemmasmallest parts functionAndrews' spt-functionHecke-Rogers series

Mathematics Subject Classification ID

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

Related Items (9)

Higher order smallest parts functions and rank-Crank moment inequalities from Bailey pairs ⋮ Exotic Bailey–Slater spt-functions III: Bailey pairs from groups B, F, G, and J ⋮ The smallest parts function associated with ω(q) ⋮ On a modularity conjecture of Andrews, Dixit, Schultz, and Yee for a variation of Ramanujan's \(\omega\)(\(q\)) ⋮ A single-variable proof of the omega SPT congruence family over powers of 5 ⋮ On spt-crank-type functions ⋮ Partitions associated with the Ramanujan/Watson mock theta functions \(\omega(q)\), \(\nu(q)\) and \(\phi(q)\) ⋮ Legendre theorems for subclasses of overpartitions ⋮ Generating functions and congruences for some partition functions related to mock theta functions

Cites Work

• Rank and crank moments for overpartitions
• Hecke modular forms and q-Hermite polynomials
• Some observations on Dyson's new symmetries of partitions
• Combinatorial interpretations of congruences for the spt-function
• Ramanujan-type partial theta identities and conjugate Bailey pairs
• Rank and conjugation for the Frobenius representation of an overpartition
• Hecke-type double sums, Appell-Lerch sums, and mock theta functions, I
• The spt-crank for overpartitions
• Hecke Modular Forms and the KAC-Peterson Identities
• RANK DIFFERENCES FOR OVERPARTITIONS
• The number of smallest parts in the partitions of n
• New Combinatorial Interpretations of Ramanujan's Partition Congruences Mod 5,7 and 11
• Dyson’s crank of a partition
• The Final Problem : An Account of the Mock Theta Functions
• Identities of the Rogers-Ramanujan Type
• A New Proof of Rogers's Transformations of Infinite Series
• Further Identities of the Rogers-Ramanujan Type
• Some Properties of Partitions
• Ramanujan's Lost Notebook
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