Inequalities Between Ranks and Cranks

Author(s)
Bringmann, Kathrin; Mahlburg, Karl Eugene
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Abstract
Higher moments of the partition rank and crank statistics have been studied for their connections to combinatorial objects such as Durfee symbols, as well as for their connections to harmonic Maass forms. This paper proves the first several cases of (and strengthens) a conjecture due to Garvan, which states that the moments of the crank function are always larger than the moments of the rank function. Furthermore, asymptotic estimates for these differences are also proven.
Date issued
2009-02
URI
http://hdl.handle.net/1721.1/49528
Department
Massachusetts Institute of Technology. Department of Mathematics
Journal
Proceedings of The American Mathematical Society
Publisher
American Mathematical Society
Citation
Bringmann, Kathrin, and Karl Mahlburg. “Inequalities between ranks and cranks.” 137 (2009): 2567-2574.
Version: Author's final manuscript
ISSN
0002-9939
1088-6826
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