Year: 2026
Type: preprint
Abstract: Recently, Garvan and Sarma studied sums of non-overlined parts in overpartitions and partitions without repeated odd parts. In this paper, we study the corresponding statistic for overlined parts. We define $\mathrm{OSOME}(n)$ as the sum of all odd overlined parts minus the sum of all even overlined parts in the overpartitions of $n$. We obtain a closed form for its generating function and use it to prove congruences by elementary $q$-series methods, the theory of half-integral weight modular forms, and known congruences for the overpartition function.
Source: arXiv (Cornell University)
Authors: Baruah, Nayandeep Deka, Gogoi, Pankaj
Institution: Tezpur University
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: University Grants Commission
OpenAlex ID: W7213955663