Unimodality of the Andrews-Garvan-Dyson cranks of partitions

DOI10.1016/j.aim.2021.108053zbMath1484.11200arXiv1811.07321OpenAlexW2900474356MaRDI QIDQ2054238

Wenston J. T. Zang, Kathy Qing Ji

Publication date: 1 December 2021

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1811.07321

zbMATH Keywords

partitionrankunimodalCrankospt-function

Mathematics Subject Classification ID

Combinatorial aspects of partitions of integers (05A17) Combinatorial inequalities (05A20) Elementary theory of partitions (11P81)

Related Items (3)

Infinite families of crank functions, Stanton-type conjectures, and unimodality ⋮ Eventual log-concavity of \(k\)-rank statistics for integer partitions ⋮ Uniform asymptotic formulas for the Fourier coefficients of the inverse of theta functions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the distribution of the \textsf{spt}-crank
• Asymptotics for \(q\)-expansions involving partial theta functions
• Proof of the Andrews-Dyson-Rhoades conjecture on the spt-crank
• Dyson's ranks and Maass forms
• Ramanujan's ``Lost Notebook. VI: The mock theta conjectures
• Partitions: At the interface of \(q\)-series and modular forms
• Nearly equal distributions of the rank and the crank of partitions
• The odd moments of ranks and cranks
• Mappings and symmetries of partitions
• Combinatorial interpretations of congruences for the spt-function
• Distribution of the partition function modulo \(m\)
• The asymptotic distribution of the rank for unimodal sequences
• Inequalities for ranks of partitions and the first moment of ranks and cranks of partitions
• The \(f(q)\) mock theta function conjecture and partition ranks
• On Dyson’s crank conjecture and the uniform asymptotic behavior of certain inverse theta functions
• The Crank of Partitions Mod 8, 9 and 10
• On the Ranks of Partitions Modulo 9
• The number of smallest parts in the partitions of n
• New Combinatorial Interpretations of Ramanujan's Partition Congruences Mod 5,7 and 11
• Dyson’s crank of a partition
• Congruence properties for the partition function
• Inequalities between ranks and cranks
• Partition congruences and the Andrews-Garvan-Dyson crank
• Ramanujan's congruences and Dyson's crank
• A new symmetry of partitions
• Some Properties of Partitions

This page was built for publication: Unimodality of the Andrews-Garvan-Dyson cranks of partitions