Infinite families of crank functions, Stanton-type conjectures, and unimodality

DOI10.1007/s40687-022-00333-3zbMath1494.11083arXiv2108.12979OpenAlexW3196887150WikidataQ123308788 ScholiaQ123308788MaRDI QIDQ2146916

Larry Rolen, Zack Tripp, Kevin Gomez, Kathrin Bringmann

Publication date: 22 June 2022

Published in: Research in the Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2108.12979

zbMATH Keywords

partitionsDyson's rankAndrews-Garvan crank

Mathematics Subject Classification ID

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

Related Items (3)

On Ramanujan-type congruences for multiplicative functions ⋮ Jacobi forms with CM and applications ⋮ Eventual log-concavity of \(k\)-rank statistics for integer partitions

Cites Work

• Unnamed Item
• Congruences for powers of the partition function
• Dyson's ranks and Maass forms
• Arithmetic properties of the partition function
• Distribution of the partition function modulo composite integers \(M\)
• Congruences in ordered pairs of partitions
• Distribution of the partition function modulo \(m\)
• Unimodality of the Andrews-Garvan-Dyson cranks of partitions
• Congruences modulo powers of 11 for some eta-quotients
• Cranks and t-cores
• On Dyson’s crank conjecture and the uniform asymptotic behavior of certain inverse theta functions
• Biranks for Partitions into 2 Colors
• The Crank of Partitions Mod 8, 9 and 10
• Generalized Frobenius partitions
• A Survey of Multipartitions Congruences and Identities
• New Combinatorial Interpretations of Ramanujan's Partition Congruences Mod 5,7 and 11
• Dyson’s crank of a partition
• Multiplicative Congruence Properties and Density Problems for p(n)
• Exceptional congruences for powers of the partition function
• Efficient implementation of the Hardy–Ramanujan–Rademacher formula
• Asymptotic formulae for partition ranks
• Some Properties of Partitions
• New congruences for the partition function

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