On the total number of parts functions associated with ranks of partitions modulo 5 and 7

DOI10.1007/s11139-021-00485-wzbMath1502.11105OpenAlexW3198292799MaRDI QIDQ2155873

Renrong Mao

Publication date: 15 July 2022

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11139-021-00485-w

zbMATH Keywords

theta-functionsAndrews-Beck-type congruencesrank for partitionstotal number of parts functions

Mathematics Subject Classification ID

Combinatorial aspects of partitions of integers (05A17) Partitions; congruences and congruential restrictions (11P83) Elementary theory of partitions (11P81)

Related Items (7)

On the total number of ones of partitions associated to cranks ⋮ Proofs of two conjectural Andrews–Beck type congruences due to Lin, Peng and Toh ⋮ Some identities on Beck's partition statistics ⋮ Andrews-Beck type congruences modulo 2 and 4 for Beck's partition statistics ⋮ Congruences for Andrews-Beck partition statistics modulo powers of primes ⋮ A modular approach to Andrews-Beck partition statistics ⋮ Some identities for Lin-Peng-Toh's \(k\)-colored partition statistic

Cites Work

• Cranks and dissections in Ramanujan's lost notebook
• Variations of Andrews-Beck type congruences
• Rank generating functions as weakly holomorphic modular forms
• New Combinatorial Interpretations of Ramanujan's Partition Congruences Mod 5,7 and 11
• Dyson’s crank of a partition
• The Components of Modular Forms
• Weighted partition rank and crank moments. III. A list of Andrews–Beck type congruences modulo 5, 7, 11 and 13
• Generalized Lambert series identities
• Some Properties of Partitions
• The Ramanujan–Dyson identities and George Beck’s congruence conjectures
• Ramanujan's Lost Notebook
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