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On Dyson's crank distribution conjecture and its generalizations


Authors: Daniel Parry and Robert C. Rhoades
Journal: Proc. Amer. Math. Soc. 145 (2017), 101-108
MSC (2010): Primary 05A16, 05A17, 11P81, 11P82
DOI: https://doi.org/10.1090/proc/13222
Published electronically: July 25, 2016
MathSciNet review: 3565363
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Abstract: Bringmann and Dousse recently established a conjecture of Dyson dealing with the limiting asymptotics of the Andrews-Garvan crank statistic for integer partitions. This note presents a direct ``sieving'' technique to establish this conjecture. The technique readily yields the analogous result for Dyson's partition rank and all of Garvan's $ k$-rank statistics.


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Additional Information

Daniel Parry
Affiliation: Department of Mathematics, Drexel University, Philadelphia, Pennsylvania 19104
Email: dtp29@drexel.edu

Robert C. Rhoades
Affiliation: Center for Communications Research, 805 Bunn Drive, Princeton, New Jersey 08540
Email: rob.rhoades@gmail.com

DOI: https://doi.org/10.1090/proc/13222
Received by editor(s): March 5, 2014
Received by editor(s) in revised form: September 25, 2014, October 12, 2015, October 14, 2015, February 15, 2016, and March 25, 2016
Published electronically: July 25, 2016
Communicated by: Ken Ono
Article copyright: © Copyright 2016 American Mathematical Society

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