Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Asymptotic inequalities for positive crank and rank moments

Authors: Kathrin Bringmann and Karl Mahlburg
Journal: Trans. Amer. Math. Soc. 366 (2014), 1073-1094
MSC (2010): Primary 11P55, 05A17
Published electronically: August 16, 2013
MathSciNet review: 3130326
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Andrews, Chan, and Kim recently introduced a modified definition of crank and rank moments for integer partitions that allows the study of both even and odd moments. In this paper, we prove the asymptotic behavior of these moments in all cases. Our main result states that the two families of moment functions are asymptotically equal, but the crank moments are also asymptotically larger than the rank moments.

Andrews, Chan, and Kim also gave a combinatorial description for the differences of the first crank and rank moments that they named the ospt-function. Our main results therefore also give the asymptotic behavior of the ospt-function (and its analogs for higher moments), and we further determine the behavior of the ospt-function modulo $ 2$ by relating its parity to Andrews' spt-function.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 11P55, 05A17

Retrieve articles in all journals with MSC (2010): 11P55, 05A17

Additional Information

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

Karl Mahlburg
Affiliation: Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803

Keywords: Integer partitions, rank, crank, Tauberian theorem
Received by editor(s): May 10, 2012
Received by editor(s) in revised form: August 14, 2012
Published electronically: August 16, 2013
Additional Notes: The research of the first author was supported by the Alfried Krupp Prize for Young University Teachers of the Krupp Foundation. The second author was supported by NSF Grant DMS-1201435.
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.