The generating functions of the rank and crank modulo 8

DOI10.1007/s11139-006-9014-4zbMath1213.11183OpenAlexW2057201689MaRDI QIDQ987523

Richard P. Lewis

Publication date: 13 August 2010

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

Full work available at URL: https://doi.org/10.1007/s11139-006-9014-4

zbMATH Keywords

partitioncrankrank

Mathematics Subject Classification ID

Partitions; congruences and congruential restrictions (11P83) Analytic theory of partitions (11P82)

Related Items (13)

On ranks and cranks of partitions modulo 4 and 8 ⋮ Identities and inequalities for the \(M_2\)-rank of partitions without repeated odd parts modulo 8 ⋮ A proof of Mao's conjecture on an identity of Beck's partition statistics ⋮ Some inequalities on cranks of cubic partitions modulo 4 and 6 ⋮ Inequalities for the \(M_2\)-rank modulo 12 of partitions without repeated odd parts ⋮ New equalities and inequalities for the ranks and cranks of partitions ⋮ FOUR IDENTITIES FOR THIRD ORDER MOCK THETA FUNCTIONS ⋮ Inequalities for ranks of partitions and the first moment of ranks and cranks of partitions ⋮ Inequalities for full rank differences of 2-marked Durfee symbols ⋮ Monotonicity properties for ranks of overpartitions ⋮ Ranks of partitions modulo 10 ⋮ Ranks, cranks for overpartitions and Appell-Lerch sums ⋮ A mock theta function identity related to the partition rank modulo 3 and 9

Cites Work

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• The Crank of Partitions Mod 8, 9 and 10
• A Combinatorial Proof of the Triple Product Identity
• Dyson’s crank of a partition
• Relations Between the Rank and the Crank Modulo 9
• Hirschhorn's identities
• On the Rank and the Crank Modulo 4 and 8
• Some properties of partitions in terms of crank
• A Simple Proof of the Quintuple Product Identity
• Some Properties of Partitions

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