On Dyson’s crank distribution conjecture and its generalizations
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- by Daniel Parry and Robert C. Rhoades
- Proc. Amer. Math. Soc. 145 (2017), 101-108
- DOI: https://doi.org/10.1090/proc/13222
- Published electronically: July 25, 2016
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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.References
Bibliographic Information
- Daniel Parry
- Affiliation: Department of Mathematics, Drexel University, Philadelphia, Pennsylvania 19104
- MR Author ID: 966636
- Email: dtp29@drexel.edu
- Robert C. Rhoades
- Affiliation: Center for Communications Research, 805 Bunn Drive, Princeton, New Jersey 08540
- MR Author ID: 762187
- Email: rob.rhoades@gmail.com
- 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
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 101-108
- MSC (2010): Primary 05A16, 05A17, 11P81, 11P82
- DOI: https://doi.org/10.1090/proc/13222
- MathSciNet review: 3565363