On some relations for the rank moduli 9 and 12

DOI10.1016/0022-314X(92)90035-NzbMath0747.11044MaRDI QIDQ1183258

Nicolas Santa-Gadea

Publication date: 28 June 1992

Published in: Journal of Number Theory (Search for Journal in Brave)

zbMATH Keywords

identitiesmock theta functionsranktheta identitiesRamanujan's partition congruences

Mathematics Subject Classification ID

Combinatorial identities, bijective combinatorics (05A19) Binomial coefficients; factorials; (q)-identities (11B65) Partitions; congruences and congruential restrictions (11P83)

Related Items (16)

On ranks and cranks of partitions modulo 4 and 8 ⋮ \(M_2\)-ranks of overpartitions modulo 4 and 8 ⋮ Generalization of Dyson's rank and non-Rogers-Ramanujan partitions ⋮ Ranks of overpartitions modulo 6 and 10 ⋮ Ramanujan-type partial theta identities and rank differences for special unimodal sequences ⋮ New equalities and inequalities for the ranks and cranks of partitions ⋮ FOUR IDENTITIES FOR THIRD ORDER MOCK THETA FUNCTIONS ⋮ Inequalities for ranks of partitions and the first moment of ranks and cranks of partitions ⋮ Ranks of overpartitions modulo 4 and 8 ⋮ RANK AND CONGRUENCES FOR OVERPARTITION PAIRS ⋮ Monotonicity properties for ranks of overpartitions ⋮ Ranks of partitions modulo 10 ⋮ \(M_2\)-ranks of overpartitions modulo 6 and 10 ⋮ The rank of a unimodal sequence and a partial theta identity of Ramanujan ⋮ Distribution of the full rank in residue classes for odd moduli ⋮ A mock theta function identity related to the partition rank modulo 3 and 9

Cites Work

• A proof of the mock theta conjectures
• Ramanujan's ``Lost Notebook. VII: The sixth order mock theta functions
• On some relations between the rank and the crank
• New Combinatorial Interpretations of Ramanujan's Partition Congruences Mod 5,7 and 11
• On the Geometry of Numbers in Elementary Number Theory
• The Final Problem : An Account of the Mock Theta Functions
• Some Properties of Partitions

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