Inequalities between ranks and cranks

DOI10.1090/S0002-9939-09-09806-2zbMath1239.11110OpenAlexW2074121962MaRDI QIDQ5322849

Kathrin Bringmann, Karl Mahlburg

Publication date: 23 July 2009

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-09-09806-2

zbMATH Keywords

partitionsasymptoticscrank momentsrank moments

Mathematics Subject Classification ID

Partitions; congruences and congruential restrictions (11P83) Elementary theory of partitions (11P81) Analytic theory of partitions (11P82)

Related Items (17)

The first positive rank and crank moments for overpartitions ⋮ Taylor coefficients of mock-Jacobi forms and moments of partition statistics ⋮ Asymptotics for rank moments of overpartitions ⋮ On the distribution of the \textsf{spt}-crank ⋮ Higher order spt-functions ⋮ Inequalities for ranks of partitions and the first moment of ranks and cranks of partitions ⋮ Mock modular forms and \(d\)-distinct partitions ⋮ Untrodden pathways in the theory of the restricted partition function \(p(n,N)\) ⋮ Asymptotic inequalities for positive crank and rank moments ⋮ ASYMPTOTICS FOR MOMENTS OF HIGHER RANKS ⋮ Asymptotic inequalities for \(k\)-ranks and their cumulation functions ⋮ Double series representations for Schur's partition function and related identities ⋮ Monotonicity properties for ranks of overpartitions ⋮ Combinatorial proofs and generalization of Bringmann, Lovejoy and Mahlburg's overpartition theorems ⋮ Unimodality of the Andrews-Garvan-Dyson cranks of partitions ⋮ An inequality between finite analogues of rank and crank moments ⋮ Asymptotics of higher order ospt-functions for overpartitions

Cites Work

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• On the explicit construction of higher deformations of partition statistics
• Partitions, Durfee symbols, and the Atkin-Garvan moments of ranks
• Dyson's ranks and Maass forms
• Relations between the ranks and cranks of partitions
• Mappings and symmetries of partitions
• Rank-crank type PDE's and non-holomorphic Jacobi forms
• Coefficients of Harmonic Maass Forms
• The number of smallest parts in the partitions of n
• Dyson’s crank of a partition
• Partition congruences and the Andrews-Garvan-Dyson crank
• Partition Statistics and Quasiharmonic Maass Forms
• Some Properties of Partitions

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