Rank differences for overpartitions

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Title: Rank differences for overpartitions
Authors: Lovejoy, Jeremy
Osburn, Robert
Permanent link: http://hdl.handle.net/10197/7946
Date: 2-Jun-2008
Online since: 2016-09-15T16:13:21Z
Abstract: In 1954, Atkin and Swinnerton-Dyer proved Dyson's conjectures on the rank of a partition by establishing formulae for the generating functions for rank differences in arithmetic progressions. In this paper, we prove formulae for the generating functions for rank differences for overpartitions. These are in terms of modular functions and generalized Lambert series.
Type of material: Journal Article
Publisher: Oxford University Press
Journal: Quarterly Journal of Mathematics
Volume: 59
Issue: 2
Start page: 257
End page: 273
Copyright (published version): 2008 Oxford University Press
Keywords: Elementary theory of partitionsPartitions of integers
DOI: 10.1093/qmath/ham031
Language: en
Status of Item: Peer reviewed
Appears in Collections:Mathematics and Statistics Research Collection

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