On Dyson’s crank distribution conjecture and its generalizations

Daniel Parry, Robert C. Rhoades

Type: Article

Publication Date: 2016-03-30

Citations: 8

DOI: https://doi.org/10.1090/proc/13222

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Proceedings of the American Mathematical Society - View

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Citing (21)

Action	Title	Year	Authors
+	The distribution of the number of summands in the partitions of a positive integer	1941	P. Erdős Joseph Lehner
+ PDF Chat	Dyson’s crank of a partition	1988	George E. Andrews Frank G. Garvan
+	On the Theorems of Watson and Dragonette for Ramanujan's Mock Theta Functions	1966	George E. Andrews
+	The f(q) mock theta function conjecture and partition ranks	2006	Kathrin Bringmann Ken Ono
+	Generalizations of Dyson's rank and non-Rogers-Ramanujan partitions	1994	Frank G. Garvan
+ PDF Chat	Unearthing the Visions of a Master: Harmonic Maass Forms and Number Theory	2008	Ken Ono
+	Basic Hypergeometric Series and Applications.	1990	Ranjan Roy N. J. Fine
+ PDF Chat	ASYMPTOTICS FOR MOMENTS OF HIGHER RANKS	2012	Matthias Waldherr
+	Ergodicity of multiplicative statistics	2012	Yu. V. Yakubovich
+ PDF Chat	Some asymptotic formulae for the mock theta series of Ramanujan	1952	Leila A. Dragonette
+ PDF Chat	Partition congruences and the Andrews-Garvan-Dyson crank	2005	Karl Mahlburg
+ PDF Chat	The structure of random partitions of large integers	1993	Bert Fristedt
+ PDF Chat	New combinatorial interpretations of Ramanujan’s partition congruences mod 5,7 and 11	1988	Frank G. Garvan
+ PDF Chat	Dyson’s ranks and Maass forms	2010	Kathrin Bringmann Ken Ono
+ PDF Chat	On Dyson’s crank conjecture and the uniform asymptotic behavior of certain inverse theta functions	2015	Kathrin Bringmann Jehanne Dousse
+	Some Properties of Partitions	1954	A. O. L. Atkin Peter Swinnerton‐Dyer
+	Asymptotic inequalities for<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mi>k</mml:mi></mml:math>-ranks and their cumulation functions	2013	Renrong Mao
+	On an Elementary Proof of Some Asymptotic Formulas in the Theory of Partitions	1942	P. Erdős
+	Taylor coefficients of mock-Jacobi forms and moments of partition statistics	2014	Kathrin Bringmann Karl Mahlburg Robert C. Rhoades
+	Ramanujan's mock theta functions and their applications (after Zwegers and Ono-Bringmann)	2009	Don Zagier
+ PDF Chat	Note on a partition limit theorem for rank and crank	2013	Persi Diaconis Svante Janson Robert C. Rhoades