A Note on Overpartition Triples

Ali H. Al-Saedi; Anaam Mutar Sharqi

doi:10.24996/ijs.2023.64.5.25

Authors

Ali H. Al-Saedi Department of Mathematics, College of Science, Mustansiriyah University, Baghdad, Iraq
Anaam Mutar Sharqi Department of Mathematics, College of Science, Mustansiriyah University, Baghdad, Iraq https://orcid.org/0000-0002-8538-5143

DOI:

https://doi.org/10.24996/ijs.2023.64.5.25

Keywords:

Partitions, Overpartitions, Overpartition triples, Congruences, Sum of divisors

Abstract

Let n be a positive integer and denotes the number of overpartition triples. In this note, we prove two identities modulo 16 and 32 for . We provide a new method to reprove a result of Lin Wang for completely determining and modulo 16. Also, we find and prove an infinite family of congruences modulo 32 for . The new method relies on expanding the fourth power of the overpartition infinite product together with the help of Gauss' identity.