The First Positive Rank and Crank Moments for Overpartitions
In 2003, Atkin and Garvan initiated the study of rank and crank moments for ordinary partitions. These moments satisfy a strict inequality. We prove that a strict inequality also holds for the first rank and crank moments of overpartitions and consider a new combinatorial interpretation in this sett...
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sg-ntu-dr.10356-840952023-02-28T19:41:33Z The First Positive Rank and Crank Moments for Overpartitions Andrews, George Chan, Song Heng Kim, Byungchan Osburn, Robert School of Physical and Mathematical Sciences Overpartitions Ranks In 2003, Atkin and Garvan initiated the study of rank and crank moments for ordinary partitions. These moments satisfy a strict inequality. We prove that a strict inequality also holds for the first rank and crank moments of overpartitions and consider a new combinatorial interpretation in this setting. Accepted version 2017-07-20T03:03:25Z 2019-12-06T15:38:15Z 2017-07-20T03:03:25Z 2019-12-06T15:38:15Z 2016 Journal Article Andrews, G., Chan, S. H., Kim, B., & Osburn, R. (2016). The First Positive Rank and Crank Moments for Overpartitions. Annals of Combinatorics, 20(2), 193-207. 0218-0006 https://hdl.handle.net/10356/84095 http://hdl.handle.net/10220/42952 10.1007/s00026-016-0306-0 en Annals of Combinatorics © 2016 Springer International Publishing. This is the author created version of a work that has been peer reviewed and accepted for publication by Annals of Combinatorics, Springer International Publishing. It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at: [http://dx.doi.org/10.1007/s00026-016-0306-0]. 14 p. application/pdf |
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Overpartitions Ranks |
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Overpartitions Ranks Andrews, George Chan, Song Heng Kim, Byungchan Osburn, Robert The First Positive Rank and Crank Moments for Overpartitions |
| description |
In 2003, Atkin and Garvan initiated the study of rank and crank moments for ordinary partitions. These moments satisfy a strict inequality. We prove that a strict inequality also holds for the first rank and crank moments of overpartitions and consider a new combinatorial interpretation in this setting. |
| author2 |
School of Physical and Mathematical Sciences |
| author_facet |
School of Physical and Mathematical Sciences Andrews, George Chan, Song Heng Kim, Byungchan Osburn, Robert |
| format |
Article |
| author |
Andrews, George Chan, Song Heng Kim, Byungchan Osburn, Robert |
| author_sort |
Andrews, George |
| title |
The First Positive Rank and Crank Moments for Overpartitions |
| title_short |
The First Positive Rank and Crank Moments for Overpartitions |
| title_full |
The First Positive Rank and Crank Moments for Overpartitions |
| title_fullStr |
The First Positive Rank and Crank Moments for Overpartitions |
| title_full_unstemmed |
The First Positive Rank and Crank Moments for Overpartitions |
| title_sort |
first positive rank and crank moments for overpartitions |
| publishDate |
2017 |
| url |
https://hdl.handle.net/10356/84095 http://hdl.handle.net/10220/42952 |
| _version_ |
1759854699896373248 |