Inequalities between ranks and cranks

Authors:
Kathrin Bringmann and Karl Mahlburg

Journal:
Proc. Amer. Math. Soc. **137** (2009), 2567-2574

MSC (2000):
Primary 11P81; Secondary 05A17

DOI:
https://doi.org/10.1090/S0002-9939-09-09806-2

Published electronically:
February 20, 2009

MathSciNet review:
2497467

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Abstract | References | Similar Articles | Additional Information

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.

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Additional Information

**Kathrin Bringmann**

Affiliation:
Mathematical Institute, University of Cologne, Weyertal 86-90, 50931 Cologne, Germany

Email:
kbringma@math.uni-koeln.de

**Karl Mahlburg**

Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307

Email:
mahlburg@math.mit.edu

DOI:
https://doi.org/10.1090/S0002-9939-09-09806-2

Received by editor(s):
October 9, 2008

Received by editor(s) in revised form:
October 20, 2008

Published electronically:
February 20, 2009

Additional Notes:
The first author was partially supported by NSF grant DMS-0757907.

The second author was partially supported by NSA Grant 6917958.

Communicated by:
Ken Ono

Article copyright:
© Copyright 2009
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.