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Article: Inequalities for full rank differences of 2-marked Durfee symbols
| Title | Inequalities for full rank differences of 2-marked Durfee symbols |
|---|---|
| Authors | |
| Keywords | k-Marked Durfee symbols Rank Partitions Ramanujan Congruences |
| Issue Date | 2012 |
| Publisher | Academic Press. The Journal's web site is located at http://www.elsevier.com/locate/issn/00973165 |
| Citation | Journal of Combinatorial Theory, Series A, 2012, v. 119 n. 2, p. 483-501 How to Cite? |
| Abstract | In this paper, we obtain infinitely many non-trivial identities and inequalities between full rank differences for 2-marked Durfee symbols, a generalization of partitions introduced by Andrews. A certain strict inequality, which almost always holds, shows that identities for Dysonʼs rank, similar to those proven by Atkin and Swinnerton-Dyer, are quite rare. By showing an analogous strict inequality, we show that such non-trivial identities are also rare for the full rank, but on the other hand we obtain an infinite family of non-trivial identities, in contrast with the partition theoretic case. |
| Persistent Identifier | http://hdl.handle.net/10722/192199 |
| ISSN | 2021 Impact Factor: 1.263 2020 SCImago Journal Rankings: 1.187 |
| ISI Accession Number ID |
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.author | Bringmann, K | en_US |
| dc.contributor.author | Kane, B | en_US |
| dc.date.accessioned | 2013-10-23T09:27:18Z | - |
| dc.date.available | 2013-10-23T09:27:18Z | - |
| dc.date.issued | 2012 | en_US |
| dc.identifier.citation | Journal of Combinatorial Theory, Series A, 2012, v. 119 n. 2, p. 483-501 | en_US |
| dc.identifier.issn | 0097-3165 | en_US |
| dc.identifier.uri | http://hdl.handle.net/10722/192199 | - |
| dc.description.abstract | In this paper, we obtain infinitely many non-trivial identities and inequalities between full rank differences for 2-marked Durfee symbols, a generalization of partitions introduced by Andrews. A certain strict inequality, which almost always holds, shows that identities for Dysonʼs rank, similar to those proven by Atkin and Swinnerton-Dyer, are quite rare. By showing an analogous strict inequality, we show that such non-trivial identities are also rare for the full rank, but on the other hand we obtain an infinite family of non-trivial identities, in contrast with the partition theoretic case. | - |
| dc.language | eng | en_US |
| dc.publisher | Academic Press. The Journal's web site is located at http://www.elsevier.com/locate/issn/00973165 | - |
| dc.relation.ispartof | Journal of Combinatorial Theory, Series A | en_US |
| dc.rights | © 2011. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ | - |
| dc.subject | k-Marked Durfee symbols | - |
| dc.subject | Rank | - |
| dc.subject | Partitions | - |
| dc.subject | Ramanujan | - |
| dc.subject | Congruences | - |
| dc.title | Inequalities for full rank differences of 2-marked Durfee symbols | en_US |
| dc.type | Article | en_US |
| dc.description.nature | postprint | - |
| dc.identifier.doi | 10.1016/j.jcta.2011.10.003 | en_US |
| dc.identifier.scopus | eid_2-s2.0-80155194872 | en_US |
| dc.identifier.volume | 119 | en_US |
| dc.identifier.issue | 2 | en_US |
| dc.identifier.spage | 483 | en_US |
| dc.identifier.epage | 501 | en_US |
| dc.identifier.isi | WOS:000297447000014 | - |
| dc.publisher.place | United States | - |
| dc.identifier.issnl | 0097-3165 | - |