On the distribution of the \textsf{spt}-crank

DOI10.3390/math1030076zbMath1296.11130OpenAlexW2048273821MaRDI QIDQ401771

Robert C. Rhoades, Freeman J. Dyson, George E. Andrews

Publication date: 27 August 2014

Published in: Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3390/math1030076

zbMATH Keywords

partitionsunimodal\textsf{spt}-crankpartition crankpartition rank

Mathematics Subject Classification ID

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

Related Items (10)

Asymptotic formulas for \(M_{2}\)-ranks of partitions without repeated odd parts ⋮ The spt-crank for overpartitions ⋮ Asymptotic formulas for spt-crank of partitions ⋮ Proof of the Andrews-Dyson-Rhoades conjecture on the spt-crank ⋮ Partition identities with mixed mock modular forms ⋮ On the non-negativity of the spt-crank for partitions without repeated odd parts ⋮ Asymptotic inequalities for \(k\)-ranks and their cumulation functions ⋮ A REMARK ON TAIL DISTRIBUTIONS OF PARTITION RANK AND CRANK ⋮ Unimodality of the Andrews-Garvan-Dyson cranks of partitions ⋮ On Dyson’s crank distribution conjecture and its generalizations

Cites Work

• Unnamed Item
• Higher order spt-functions
• Modular forms and quantum invariants of \(3\)-manifolds
• The odd moments of ranks and cranks
• Partitions and the grand canonical ensemble
• Combinatorial interpretations of congruences for the spt-function
• Taylor coefficients of mock-Jacobi forms and moments of partition statistics
• CRANK 0 PARTITIONS AND THE PARITY OF THE PARTITION FUNCTION
• The Dilogarithm Function
• The number of smallest parts in the partitions of n
• CONGRUENCES FOR ANDREWS' SMALLEST PARTS PARTITION FUNCTION AND NEW CONGRUENCES FOR DYSON'S RANK
• New Combinatorial Interpretations of Ramanujan's Partition Congruences Mod 5,7 and 11
• Dyson’s crank of a partition
• Self-conjugate vector partitions and the parity of the spt-function
• Note on a partition limit theorem for rank and crank
• Asymptotics for rank and crank moments
• Inequalities between ranks and cranks
• STACKS (II)
• Some Properties of Partitions

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