Inequalities Between Ranks and Cranks
Author(s)Bringmann, Kathrin; Mahlburg, Karl Eugene
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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.
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Proceedings of The American Mathematical Society
American Mathematical Society
Bringmann, Kathrin, and Karl Mahlburg. “Inequalities between ranks and cranks.” 137 (2009): 2567-2574.
Author's final manuscript