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Article: Inequalities for full rank differences of 2-marked Durfee symbols

TitleInequalities for full rank differences of 2-marked Durfee symbols
Authors
Keywordsk-Marked Durfee symbols
Rank
Partitions
Ramanujan
Congruences
Issue Date2012
Citation
Journal of Combinatorial Theory. Series A, 2012, v. 119 n. 2, p. 483-501 How to Cite?
AbstractIn 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 Identifierhttp://hdl.handle.net/10722/192199
ISSN
2015 Impact Factor: 0.979
2015 SCImago Journal Rankings: 2.350
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorBringmann, Ken_US
dc.contributor.authorKane, Ben_US
dc.date.accessioned2013-10-23T09:27:18Z-
dc.date.available2013-10-23T09:27:18Z-
dc.date.issued2012en_US
dc.identifier.citationJournal of Combinatorial Theory. Series A, 2012, v. 119 n. 2, p. 483-501en_US
dc.identifier.issn0097-3165en_US
dc.identifier.urihttp://hdl.handle.net/10722/192199-
dc.description.abstractIn 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.languageengen_US
dc.relation.ispartofJournal of Combinatorial Theory. Series Aen_US
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.subjectk-Marked Durfee symbols-
dc.subjectRank-
dc.subjectPartitions-
dc.subjectRamanujan-
dc.subjectCongruences-
dc.titleInequalities for full rank differences of 2-marked Durfee symbolsen_US
dc.typeArticleen_US
dc.description.naturepostprint-
dc.identifier.doi10.1016/j.jcta.2011.10.003en_US
dc.identifier.scopuseid_2-s2.0-80155194872en_US
dc.identifier.volume119en_US
dc.identifier.issue2en_US
dc.identifier.spage483en_US
dc.identifier.epage501en_US
dc.identifier.isiWOS:000297447000014-

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