The rank and crank of partitions modulo 3

DOI10.1142/S1793042116500640zbMath1336.05012MaRDI QIDQ2805969

Renrong Mao, Song Heng Chan

Publication date: 13 May 2016

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

zbMATH Keywords

partitionscrankinequalitiesgenerating functionsDyson's rankgeneralized Lambert series

Mathematics Subject Classification ID

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

Related Items (8)

On a generalized crank for \(k\)-colored partitions ⋮ On cranks of partitions modulo 12 and 16 ⋮ New equalities and inequalities for the ranks and cranks of partitions ⋮ FOUR IDENTITIES FOR THIRD ORDER MOCK THETA FUNCTIONS ⋮ On a sign pattern for the crank function of cubic partition pairs ⋮ On three identities of Ramanujan ⋮ Some inequalities for Garvan's bicrank function of 2-colored partitions ⋮ A mock theta function identity related to the partition rank modulo 3 and 9

Cites Work

• Unnamed Item
• \(M_2\)-rank differences for partitions without repeated odd parts
• Cranks and dissections in Ramanujan's lost notebook
• Inequalities for ranks of partitions and the first moment of ranks and cranks of partitions
• Hecke-type double sums, Appell-Lerch sums, and mock theta functions, I
• The Crank of Partitions Mod 8, 9 and 10
• Some Properties of Partitions
• New Combinatorial Interpretations of Ramanujan's Partition Congruences Mod 5,7 and 11
• Relations Between the Rank and the Crank Modulo 9
• On the Rank and the Crank Modulo 4 and 8
• Some Properties of Partitions

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