Combinatorial identities associated with a bivariate generating function for overpartition pairs

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dc.contributor.author Dixit, Atul
dc.contributor.author Goswami, Ankush
dc.coverage.spatial
dc.date.accessioned 2022-02-03T08:03:07Z
dc.date.available 2022-02-03T08:03:07Z
dc.date.issued 2022-01
dc.identifier.citation Dixit, Atul and Goswami, Ankush, "Combinatorial identities associated with a bivariate generating function for overpartition pairs", arXiv, Cornell University Library, DOI: arXiv:2201.06746, Jan. 2022. en_US
dc.identifier.issn
dc.identifier.uri https://arxiv.org/abs/2201.06746
dc.identifier.uri https://repository.iitgn.ac.in/handle/123456789/7455
dc.description.abstract We obtain a three-parameter q-series identity that generalizes two results of Chan and Mao. By specializing our identity, we derive new results of combinatorial significance in connection with N(r,s,m,n), a function counting certain overpartition pairs recently introduced by Bringmann, Lovejoy and Osburn. For example, one of our identities gives a closed-form evaluation of a double series in terms of Chebyshev polynomials of the second kind, thereby resulting in an analogue of Euler's pentagonal number theorem. Another of our results expresses a multi-sum involving N(r,s,m,n) in terms of just the partition function p(n). Using a result of Shimura we also relate a certain double series with a weight 7/2 theta series.
dc.description.statementofresponsibility by Atul Dixit and Ankush Goswami
dc.language.iso en_US en_US
dc.publisher Cornell University Library en_US
dc.subject Combinatorial identities en_US
dc.subject Combinatorics en_US
dc.subject Number Theory en_US
dc.subject Partition function en_US
dc.subject Chebyshev polynomials en_US
dc.title Combinatorial identities associated with a bivariate generating function for overpartition pairs en_US
dc.type Pre-Print en_US
dc.relation.journal arXiv


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