On Dyson’s crank distribution conjecture and its generalizations

DOI10.1090/proc/13222zbMath1350.05008OpenAlexW2322555227WikidataQ123351555 ScholiaQ123351555MaRDI QIDQ2832810

Robert C. Rhoades, Daniel T. Parry

Publication date: 14 November 2016

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

Full work available at URL: https://doi.org/10.1090/proc/13222

zbMATH Keywords

Dyson's partition rankGarvan's \(k\)-rank statisticssieving technique

Mathematics Subject Classification ID

Combinatorial aspects of partitions of integers (05A17) Elementary theory of partitions (11P81) Asymptotic enumeration (05A16) Analytic theory of partitions (11P82)

Related Items (9)

Asymptotic formulas for \(M_{2}\)-ranks of partitions without repeated odd parts ⋮ Integer partitions, probabilities and quantum modular forms ⋮ On the asymptotic behavior of unimodal rank generating functions ⋮ Asymptotic formulas for spt-crank of partitions ⋮ Asymptotics for \(q\)-expansions involving partial theta functions ⋮ The asymptotic profile of an eta-theta quotient related to entanglement entropy in string theory ⋮ ON THE DISTRIBUTION OF THE RANK STATISTIC FOR STRONGLY CONCAVE COMPOSITIONS ⋮ On the distribution of rank and crank statistics for integer partitions ⋮ Uniform asymptotic formulas for the Fourier coefficients of the inverse of theta functions

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