Generalization of Dyson's rank and non-Rogers-Ramanujan partitions

DOI10.1007/BF02567461zbMath0819.11043MaRDI QIDQ1340661

Frank G. Garvan

Publication date: 25 January 1995

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/155995

zbMATH Keywords

partitionscrank\(k\)-rank\(k\)-conjugationnumber of self-\(2k\)- conjugate partitions

Mathematics Subject Classification ID

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

Related Items (22)

Generalized higher order spt-functions ⋮ Rank-crank-type PDEs and generalized Lambert series identities ⋮ The Bailey chain and mock theta functions ⋮ Iteration process for multiple Rogers-Ramanujan identities ⋮ Eventual log-concavity of \(k\)-rank statistics for integer partitions ⋮ An extension to overpartitions of the Rogers-Ramanujan identities for even moduli ⋮ Dyson's new symmetry and generalized Rogers-Ramanujan identities ⋮ Partition identities involving gaps and weights ⋮ Partitions, Durfee symbols, and the Atkin-Garvan moments of ranks ⋮ Variations of Andrews-Beck type congruences ⋮ ASYMPTOTICS FOR MOMENTS OF HIGHER RANKS ⋮ Asymptotic inequalities for \(k\)-ranks and their cumulation functions ⋮ A combinatorial proof of the Rogers--Ramanujan and Schur identities ⋮ Mock modularity of the \(M_{d}\)-rank of overpartitions ⋮ Asymptotics for rank partition functions ⋮ On the distribution of rank and crank statistics for integer partitions ⋮ On Dyson’s crank distribution conjecture and its generalizations ⋮ \(M_2\)-rank differences for partitions without repeated odd parts ⋮ Generalizations of Dyson’s rank on overpartitions ⋮ Some observations on Dyson's new symmetries of partitions ⋮ Uniform asymptotic formulas for the Fourier coefficients of the inverse of theta functions ⋮ THE SECOND SHIFTED DIFFERENCE OF PARTITIONS AND ITS APPLICATIONS

Cites Work

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• Multiple series Rogers-Ramanujan type identities
• A proof of the mock theta conjectures
• On the seventh order mock theta functions
• Ramanujan's ``Lost Notebook. VI: The mock theta conjectures
• On some relations for the rank moduli 9 and 12
• On some relations between the rank and the crank
• Mappings and symmetries of partitions
• Cranks and t-cores
• The Crank of Partitions Mod 8, 9 and 10
• A Combinatorial Generalization of the Rogers-Ramanujan Identities
• New Combinatorial Interpretations of Ramanujan's Partition Congruences Mod 5,7 and 11
• Dyson’s crank of a partition
• Relations Between the Rank and the Crank Modulo 9
• Partitions and Durfee Dissection
• A new symmetry of partitions
• The Final Problem : An Account of the Mock Theta Functions
• A New Proof of Rogers's Transformations of Infinite Series
• Further Identities of the Rogers-Ramanujan Type
• Some Properties of Partitions

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