Document Type
Article
Abstract
The study of overpartitions in recent years has been used to great effect in various fields, including hypergeometric series, q-series identities, and mathematical physics. We investigate the limiting distributions of the number of parts in a family of overpartitions of n, introduced by Andrews, where parts are counted with two different weights. Using Andrews’ identities and the saddle-point method, we establish two central limit theorems (CLTs) for the number of parts as n → ∞, corresponding to these weightings. We also derive explicit formulas for the mean and variance in each case.
Digital Object Identifier (DOI)
Publication Info
Published in The Ramanujan Journal, Volume 69, 2026.
APA Citation
Bhowmik, T., Cao, A., Frew, J., Lehman, J., & Tsai, W.-L. (2026). Limit theorems for Andrews’ restricted overpartitions. The Ramanujan Journal, 69.https://doi.org/10.1007/s11139-025-01313-1
Rights
© The Author(s) 2026 This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.