Universität zu Köln

Bringmann, Kathrin ORCID: 0000-0001-7126-1409 and Mahlburg, Karl (2014). ASYMPTOTIC INEQUALITIES FOR POSITIVE CRANK AND RANK MOMENTS. Trans. Am. Math. Soc., 366 (2). S. 1073 - 1095. PROVIDENCE: AMER MATHEMATICAL SOC. ISSN 1088-6850

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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.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Bringmann, Kathrin UNSPECIFIED orcid.org/0000-0001-7126-1409 UNSPECIFIED Mahlburg, Karl UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-448024
Journal or Publication Title:	Trans. Am. Math. Soc.
Volume:	366
Number:	2
Page Range:	S. 1073 - 1095
Date:	2014
Publisher:	AMER MATHEMATICAL SOC
Place of Publication:	PROVIDENCE
ISSN:	1088-6850
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Mathematics and Computer Science > Mathematical Institute
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language PARTITION CONGRUENCES Multiple languages Mathematics Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/44802