scholarly journals Relations Between the Ranks and Cranks of Partitions

2003 ◽  
pp. 343-366
Author(s):  
A. O. L. Atkin ◽  
F. G. Garvan
Keyword(s):  
Cranks Of Partitions

Asymptotics for rank moments of overpartitions

2014 ◽  
Vol 10 (08) ◽  
pp. 2011-2036 ◽  
Author(s):  
Renrong Mao
Keyword(s):  
Asymptotic Formulas ◽  
Error Terms ◽  
Cranks Of Partitions

Bringmann, Mahlburg and Rhoades proved asymptotic formulas for all the even moments of the ranks and cranks of partitions with polynomial error terms. In this paper, motivated by their work, we apply the same method and obtain asymptotics for the two rank moments of overpartitions.

scholarly journals On ranks and cranks of partitions modulo 4 and 8

2019 ◽  
Vol 161 ◽  
pp. 51-80 ◽  
Author(s):  
Eric T. Mortenson
Keyword(s):  
Cranks Of Partitions

scholarly journals The Ranks and Cranks of Partitions Moduli 2, 3, and 4

2000 ◽  
Vol 85 (1) ◽  
pp. 74-84 ◽  
Author(s):  
George A Andrews ◽  
Richard Lewis
Keyword(s):  
Cranks Of Partitions

scholarly journals Unimodality of the Andrews-Garvan-Dyson cranks of partitions

2021 ◽  
Vol 393 ◽  
pp. 108053
Author(s):  
Kathy Q. Ji ◽  
Wenston J.T. Zang
Keyword(s):  
Cranks Of Partitions

A mock theta function identity related to the partition rank modulo 3 and 9

2020 ◽  
pp. 1-17
Author(s):  
Song Heng Chan ◽  
Nankun Hong ◽  
Jerry ◽  
Jeremy Lovejoy
Keyword(s):  
Generating Function ◽  
Theta Function ◽  
Generating Functions ◽  
Mock Theta Function ◽  
Function Identity ◽  
Theta Function Identity ◽  
Cranks Of Partitions

We prove a new mock theta function identity related to the partition rank modulo 3 and 9. As a consequence, we obtain the [Formula: see text]-dissection of the rank generating function modulo [Formula: see text]. We also evaluate all of the components of the rank–crank differences modulo [Formula: see text]. These are analogous to conjectures of Lewis [The generating functions of the rank and crank modulo 8, Ramanujan J. 18 (2009) 121–146] on rank–crank differences modulo [Formula: see text], first proved by Mortenson [On ranks and cranks of partitions modulo 4 and 8, J. Combin. Theory Ser. A 161 (2019) 51–80].

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