A Note on Overpartition Triples

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.

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