Modulo d extension of parity results in Rogers-Ramanujan-Gordon type overpartition identities

Kurşungöz, Kağan and Zadeh Dabbagh, Mohammad (2023) Modulo d extension of parity results in Rogers-Ramanujan-Gordon type overpartition identities. International Journal of Number Theory . ISSN 1793-0421 Published Online First https://dx.doi.org/10.1142/S1793042123500884

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Abstract

Sang, Shi and Yee, in 2020, found overpartition analogs of Andrews' results involving parity in Rogers-Ramanujan-Gordon identities. Their result partially answered an open question of Andrews'. The open question was to involve parity in overpartition identities. We extend Sang, Shi and Yee's work to arbitrary moduli, and also provide a missing case in their identities. We also unify proofs of Rogers-Ramanujan-Gordon identities for overpartitions due to Lovejoy and Chen et al.; Sang, Shi and Yee's results; and ours. Although verification type proofs are given for brevity, a construction of series as solutions of functional equations between partition generating functions is sketched.
Item Type: Article
Uncontrolled Keywords: Integer partition; overpartition; partition generating function; Rogers-Ramanujan type partition identity
Divisions: Faculty of Engineering and Natural Sciences
Depositing User: Kağan Kurşungöz
Date Deposited: 07 Aug 2023 14:51
Last Modified: 07 Aug 2023 14:51
URI: https://research.sabanciuniv.edu/id/eprint/47435

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