Combinatorial interpretations of cranks of overpartitions and partitions without repeated odd parts

DOI10.3842/SIGMA.2024.097MaRDI QIDQ6646232

Frank G. Garvan, Rishabh Sarma

Publication date: 29 November 2024

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

zbMATH Keywords

overpartitionsresidual crank

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) (q)-calculus and related topics (05A30) Combinatorial aspects of partitions of integers (05A17) Partitions; congruences and congruential restrictions (11P83) Elementary theory of partitions (11P81)

Cites Work

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• Rank and crank moments for overpartitions
• \(M_2\)-rank differences for partitions without repeated odd parts
• A proof of the mock theta conjectures
• Ramanujan's ``Lost Notebook. VI: The mock theta conjectures
• Tenth order mock theta functions in Ramanujan's lost notebook
• Some observations on Dyson's new symmetries of partitions
• The spt-crank for overpartitions
• M₂-rank differences for overpartitions
• RANK DIFFERENCES FOR OVERPARTITIONS
• Weakly holomorphic modular forms of half-integral weight with nonvanishing constant terms modulo $\ell $
• New Combinatorial Interpretations of Ramanujan's Partition Congruences Mod 5,7 and 11
• Dyson’s crank of a partition
• Overpartitions
• Some Properties of Partitions
• Tenth order mock theta functions in Ramanujan's lost notebook. II
• Overpartition rank differences modulo 7 by Maass forms

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